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Merge pull request LMFDB#6282 from fchapoton/doc_siegel_from_html_to_rst
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turn doc in bad file into rst syntax (roughly)
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@edgarcosta
edgarcosta authored Dec 2, 2024
2 parents 2b34a39 + 497663e commit 55bf75b
Showing 1 changed file with 91 additions and 112 deletions.
203 changes: 91 additions & 112 deletions lmfdb/siegel_modular_forms/dimensions.py
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Original file line number Diff line number Diff line change
Expand Up @@ -54,91 +54,76 @@ def parse_dim_args(dim_args, default_dim_args):

def dimension_Gamma_2(wt_range, j):
r"""
<ul>
<li>First entry of the respective triple: The full space.</li>
<li>Second entry: The codimension of the subspace of cusp forms.</li>
<li>Third entry: The subspace of cusp forms.</li>
</ul>
<p> More precisely, The triple $[a,b,c]$ in
<ul>
<li>
row <span class="emph">All</span>
and in the $k$th column shows the dimension of
the full space $M_{k,j}(\Gamma(2))$,
of the non cusp forms, and of the cusp forms.</li>
<li>
in row <span class="emph">$p$</span>, where $p$ is a partition of $6$,
and in the $k$th column shows the multiplicity of the
$\mathrm{Sp}(4,\Z)$-representation
associated to $p$ in the full $\mathrm{Sp}(4,\Z)$-module
$M_{k,j}(\Gamma(2))$,
in the submodule of non cusp forms and of cusp forms.
(See below for details.)
</li>
</ul>
First entry of the respective triple: The full space.
Second entry: The codimension of the subspace of cusp forms.
Third entry: The subspace of cusp forms.
More precisely, The triple $[a,b,c]$ in
row All
and in the $k$th column shows the dimension of
the full space $M_{k,j}(\Gamma(2))$,
of the non cusp forms, and of the cusp forms.
in row $p$, where $p$ is a partition of $6$,
and in the $k$th column shows the multiplicity of the
$\mathrm{Sp}(4,\Z)$-representation
associated to $p$ in the full $\mathrm{Sp}(4,\Z)$-module
$M_{k,j}(\Gamma(2))$,
in the submodule of non cusp forms and of cusp forms.
(See below for details.)
"""
return _dimension_Gamma_2(wt_range, j, group='Gamma(2)')


def dimension_Gamma1_2(wt_range, j):
r"""
<ul>
<li>First entry of the respective triple: The full space.</li>
<li>Second entry: The codimension of the subspace of cusp forms.</li>
<li>Third entry: The subspace of cusp forms.</li>
</ul>
<p> More precisely, The triple $[a,b,c]$ in
<ul>
<li>
row <span class="emph">All</span>
and in the $k$th column shows the dimension of
the full space $M_{k,j}(\Gamma(2))$,
of the non cusp forms, and of the cusp forms.</li>
<li>
in row <span class="emph">$p$</span>, where $p$ is a partition of $3$,
and in the $k$th column shows the multiplicity of the
$\Gamma_1(2)$-representation
associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$,
in the submodule of non cusp forms and of cusp forms.
(See below for details.)
</li>
</ul>
First entry of the respective triple: The full space.
Second entry: The codimension of the subspace of cusp forms.
Third entry: The subspace of cusp forms.
More precisely, The triple $[a,b,c]$ in
row All
and in the $k$th column shows the dimension of
the full space $M_{k,j}(\Gamma(2))$,
of the non cusp forms, and of the cusp forms.
in row $p$, where $p$ is a partition of $3$,
and in the $k$th column shows the multiplicity of the
$\Gamma_1(2)$-representation
associated to $p$ in the full $\Gamma_1(2)$-module $M_{k,j}(\Gamma(2))$,
in the submodule of non cusp forms and of cusp forms.
(See below for details.)
"""
return _dimension_Gamma_2(wt_range, j, group='Gamma1(2)')


def dimension_Gamma0_2(wt_range, j):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.</li>
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.
<span class="emph">Cusp</span>: The subspace of cusp forms.
"""
return _dimension_Gamma_2(wt_range, j, group='Gamma0(2)')


def dimension_Sp4Z(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Eisenstein</span>: The subspace of Siegel Eisenstein series.</li>
<li><span class="emph">Klingen</span>: The subspace of Klingen Eisenstein series.</li>
<li><span class="emph">Maass</span>: The subspace of Maass liftings.</li>
<li><span class="emph">Interesting</span>: The subspace spanned by cuspidal eigenforms that are not Maass liftings.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Eisenstein</span>: The subspace of Siegel Eisenstein series.
<span class="emph">Klingen</span>: The subspace of Klingen Eisenstein series.
<span class="emph">Maass</span>: The subspace of Maass liftings.
<span class="emph">Interesting</span>: The subspace spanned by cuspidal eigenforms that are not Maass liftings.
"""
return _dimension_Sp4Z(wt_range)


def dimension_Sp4Z_2(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Non cusp</span>: The subspace of non cusp forms.</li>
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Non cusp</span>: The subspace of non cusp forms.
<span class="emph">Cusp</span>: The subspace of cusp forms.
"""
return _dimension_Gamma_2(wt_range, 2, group='Sp4(Z)')

Expand All @@ -160,11 +145,9 @@ def dimension_table_Sp4Z_j(wt_range, j_range):

def dimension_Sp4Z_j(wt_range, j):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Non cusp</span>: The subspace of non cusp forms.</li>
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Non cusp</span>: The subspace of non cusp forms.
<span class="emph">Cusp</span>: The subspace of cusp forms.
"""
return _dimension_Gamma_2(wt_range, j, group='Sp4(Z)')

Expand Down Expand Up @@ -307,12 +290,10 @@ def _dimension_Gamma_2(wt_range, j, group='Gamma(2)'):

def dimension_Sp6Z(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Miyawaki lifts I</span>: The subspace of Miyawaki lifts of type I.</li>
<li><span class="emph">Miyawaki lifts II</span>: The subspace of (conjectured) Miyawaki lifts of type II.</li>
<li><span class="emph">Other</span>: The subspace of cusp forms which are not Miyawaki lifts of type I or II.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Miyawaki lifts I</span>: The subspace of Miyawaki lifts of type I.
<span class="emph">Miyawaki lifts II</span>: The subspace of (conjectured) Miyawaki lifts of type II.
<span class="emph">Other</span>: The subspace of cusp forms which are not Miyawaki lifts of type I or II.
"""
return _dimension_Sp6Z(wt_range)

Expand Down Expand Up @@ -365,12 +346,10 @@ def __dimension_Sp6Z(wt):

def dimension_Sp8Z(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The subspace of cusp forms.</li>
<li><span class="emph">Ikeda lifts</span>: The subspace of Ikeda lifts.</li>
<li><span class="emph">Miyawaki lifts</span>: The subspace of Miyawaki lifts.</li>
<li><span class="emph">Other</span>: The subspace that are not Ikeda or Miyawaki lifts.</li>
</ul>
<span class="emph">Total</span>: The subspace of cusp forms.
<span class="emph">Ikeda lifts</span>: The subspace of Ikeda lifts.
<span class="emph">Miyawaki lifts</span>: The subspace of Miyawaki lifts.
<span class="emph">Other</span>: The subspace that are not Ikeda or Miyawaki lifts.
"""
headers = ['Total', 'Ikeda lifts', 'Miyawaki lifts', 'Other']
dct = {}
Expand Down Expand Up @@ -429,11 +408,9 @@ def _dimension_Sp8Z(wt):

def dimension_Gamma0_4_half(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
<li><span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.</li>
<li><span class="emph">Cusp</span>: The subspace of cusp forms.</li>
</ul>
<span class="emph">Total</span>: The full space.
<span class="emph">Non cusp</span>: The codimension of the subspace of cusp forms.
<span class="emph">Cusp</span>: The subspace of cusp forms.
"""
headers = ['Total', 'Non cusp', 'Cusp']
dct = {}
Expand All @@ -449,14 +426,17 @@ def _dimension_Gamma0_4_half(k):
of half integral weight k - 1/2.
INPUT
The realweight is k-1/2
The realweight is k-1/2
OUTPUT
('Total', 'Non cusp', 'Cusp')
('Total', 'Non cusp', 'Cusp')
REMARK
Note that formula from Hayashida's and Ibukiyama's paper has formula
that coefficient of x^w is for weight (w+1/2). So here w=k-1.
Note that formula from Hayashida's and Ibukiyama's paper has formula
that coefficient of x^w is for weight (w+1/2). So here w=k-1.
"""
if k < 1:
raise ValueError("$k$ must be a positive integer")
Expand All @@ -475,9 +455,7 @@ def _dimension_Gamma0_4_half(k):

def dimension_Gamma0_3_psi_3(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
</ul>
<span class="emph">Total</span>: The full space.
"""
headers = ['Total']
dct = {}
Expand All @@ -493,10 +471,12 @@ def _dimension_Gamma0_3_psi_3(wt):
on $Gamma_0(3)$ with character $\psi_3$.
OUTPUT
("Total")
("Total")
REMARK
Not completely implemented
Not completely implemented
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
Expand All @@ -515,10 +495,9 @@ def _dimension_Gamma0_3_psi_3(wt):

def dimension_Gamma0_4_psi_4(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
</ul>
<p> Odd weights are not yet implemented.</p>
<span class="emph">Total</span>: The full space.
Odd weights are not yet implemented.
"""
headers = ['Total']
dct = {}
Expand All @@ -537,10 +516,12 @@ def _dimension_Gamma0_4_psi_4(wt):
with character $\psi_4$.
OUTPUT
("Total")
("Total")
REMARK
The formula for odd weights is unknown or not obvious from the paper.
The formula for odd weights is unknown or not obvious from the paper.
"""
R = PowerSeriesRing(ZZ, default_prec=wt + 1, names=('x',))
(x,) = R._first_ngens(1)
Expand All @@ -556,9 +537,7 @@ def _dimension_Gamma0_4_psi_4(wt):

def dimension_Gamma0_4(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
</ul>
<span class="emph">Total</span>: The full space.
"""
headers = ['Total']
dct = {}
Expand All @@ -573,10 +552,12 @@ def _dimension_Gamma0_4(wt):
Return the dimensions of subspaces of Siegel modular forms on $Gamma0(4)$.
OUTPUT
("Total",)
("Total",)
REMARK
Not completely implemented
Not completely implemented
"""
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(wt + 1)
Expand All @@ -590,9 +571,7 @@ def _dimension_Gamma0_4(wt):

def dimension_Gamma0_3(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The full space.</li>
</ul>
<span class="emph">Total</span>: The full space.
"""
headers = ['Total']
dct = {}
Expand All @@ -607,10 +586,12 @@ def _dimension_Gamma0_3(wt):
Return the dimensions of subspaces of Siegel modular forms on $Gamma0(3)$.
OUTPUT
("Total")
("Total")
REMARK
Only total dimension implemented.
Only total dimension implemented.
"""
R = PowerSeriesRing(ZZ, 'x')
x = R.gen().O(wt + 1)
Expand All @@ -624,11 +605,9 @@ def _dimension_Gamma0_3(wt):

def dimension_Dummy_0(wt_range):
"""
<ul>
<li><span class="emph">Total</span>: The subspace of cusp forms.</li>
<li><span class="emph">Yoda lifts</span>: The subspace of Master Yoda lifts.</li>
<li><span class="emph">Hinkelstein series</span>: The subspace of Hinkelstein series.</li>
</ul>
<span class="emph">Total</span>: The subspace of cusp forms.
<span class="emph">Yoda lifts</span>: The subspace of Master Yoda lifts.
<span class="emph">Hinkelstein series</span>: The subspace of Hinkelstein series.
"""
headers = ['Total', 'Yoda lifts', 'Hinkelstein series']
dct = {}
Expand Down

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