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
class sage.modular.modform.submodule.ModularFormsSubmodule(ambient_module, submodule, dual=None, check=False)

Bases: sage.modular.modform.space.ModularFormsSpace, sage.modular.hecke.submodule.HeckeSubmodule

A submodule of an ambient space of modular forms.

class sage.modular.modform.submodule.ModularFormsSubmoduleWithBasis(ambient_module, submodule, dual=None, check=False)

Bases: sage.modular.modform.submodule.ModularFormsSubmodule

INPUT:

  • ambient_module – ModularFormsSpace

  • submodule – a submodule of the ambient space.

  • dual_module – (default: None) ignored

  • check – (default: False) whether to check that the

    submodule is Hecke equivariant

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

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