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  • src/sage/modular/quasimodform

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src/sage/modular/quasimodform/ring.py

Lines changed: 13 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -781,7 +781,16 @@ def from_polynomial(self, polynomial):
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def basis_of_weight(self, weight):
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r"""
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Return a basis of elements generating the subspace of the given weight.
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Return a basis of elements generating the subspace of the given
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weight.
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INPUT:
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- ``weight`` (integer) -- the weight of the subspace
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OUTPUT:
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A list of quasimodular forms of the given weight.
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EXAMPLES::
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@@ -806,8 +815,10 @@ def basis_of_weight(self, weight):
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"""
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basis = []
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E2 = self.weight_2_eisenstein_series()
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M = self.__modular_forms_subring
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for j in range(weight//2):
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basis += [f*E2**j for f in self.__modular_forms_subring.modular_forms_of_weight(weight - 2*j).basis()]
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basis += [f*E2**j for f
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in M.modular_forms_of_weight(weight - 2*j).basis()]
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if not weight%2:
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basis.append(E2**(Integer(weight/2)))
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return basis

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