implement the depth of a quasimodular form

src/sage/modular/quasimodform/element.py

@@ -294,6 +294,45 @@ def __bool__(self):
         """
         return bool(self._polynomial)
 
+    def depth(self):
+        r"""
+        Return the depth of the given quasimodular form.
+
+        Note that the quasimodular form must be homogeneous of weight
+        `k`. Recall that the *depth* is the integer `p` such that
+
+        .. MATH::
+
+            f = f_0 + f_1 E_2 + \cdots + f_p E_2^p,
+
+        where `f_i` is a modular form of weight `k - 2i` and `f_p` is
+        nonzero.
+
+        EXAMPLES::
+
+            sage: QM = QuasiModularForms(1)
+            sage: E2, E4, E6 = QM.gens()
+            sage: E2.depth()
+            1
+            sage: F = E4^2 + E6*E2 + E4*E2^2 + E2^4
+            sage: F.depth()
+            4
+            sage: QM(7/11).depth()
+            0
+
+        TESTS::
+
+            sage: QM = QuasiModularForms(1)
+            sage: (QM.0 + QM.1).depth()
+            Traceback (most recent call last):
+            ...
+            ValueError: the given graded quasiform is not an homogeneous element
+        """
+        if not self.is_homogeneous():
+            raise ValueError("the given graded quasiform is not an "
+                             "homogeneous element")
+        return self._polynomial.degree()
+
     def is_zero(self):
         r"""
         Return whether the given quasimodular form is zero.