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# 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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