Submodules of spaces of modular forms¶
EXAMPLES:
sage: M = ModularForms(Gamma1(13),2); M
Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
sage: M.eisenstein_subspace()
Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
sage: M == loads(dumps(M))
True
sage: M.cuspidal_subspace()
Cuspidal subspace of dimension 2 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
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class
sage.modular.modform.submodule.ModularFormsSubmodule(ambient_module, submodule, dual=None, check=False)¶ Bases:
sage.modular.modform.space.ModularFormsSpace,sage.modular.hecke.submodule.HeckeSubmoduleA submodule of an ambient space of modular forms.
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class
sage.modular.modform.submodule.ModularFormsSubmoduleWithBasis(ambient_module, submodule, dual=None, check=False)¶