Submodules of spaces of modular forms - Modular Forms

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# Submodules of spaces of modular forms

EXAMPLES:

Sage

    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

Python

    >>> from sage.all import *
    >>> M = ModularForms(Gamma1(Integer(13)),Integer(2)); M
    Modular Forms space of dimension 13 for
     Congruence Subgroup Gamma1(13) of weight 2 over Rational Field
    >>> 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
    >>> M == loads(dumps(M))
    True
    >>> 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: `ModularFormsSpace`, `HeckeSubmodule`

  A submodule of an ambient space of modular forms.

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

  Bases: `ModularFormsSubmodule`