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# Modular Forms for \(\Gamma_0(N)\) over \(\QQ\)

TESTS:

    sage: m = ModularForms(Gamma0(389),6)
    sage: loads(dumps(m)) == m
    True

class `sage.modular.modform.ambient_g0.``ModularFormsAmbient_g0_Q`(level, weight)

  Bases: `sage.modular.modform.ambient.ModularFormsAmbient`

  A space of modular forms for \(\Gamma_0(N)\) over \(\QQ\).

  `cuspidal_submodule`()

    Return the cuspidal submodule of this space of modular forms for \(\Gamma_0(N)\).

    EXAMPLES:

        sage: m = ModularForms(Gamma0(33),4)
        sage: s = m.cuspidal_submodule(); s
        Cuspidal subspace of dimension 10 of Modular Forms space of dimension 14 for Congruence Subgroup Gamma0(33) of weight 4 over Rational Field
        sage: type(s)
        <class 'sage.modular.modform.cuspidal_submodule.CuspidalSubmodule_g0_Q_with_category'>

  `eisenstein_submodule`()

    Return the Eisenstein submodule of this space of modular forms for \(\Gamma_0(N)\).

    EXAMPLES:

        sage: m = ModularForms(Gamma0(389),6)
        sage: m.eisenstein_submodule()
        Eisenstein subspace of dimension 2 of Modular Forms space of dimension 163 for Congruence Subgroup Gamma0(389) of weight 6 over Rational Field

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