Module: sage.modular.modform.ambient_g1
Modular Forms for
over
.
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: S = M.cuspidal_submodule(); S Cuspidal subspace of dimension 2 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field sage: S.basis() [ q - 4*q^3 - q^4 + 3*q^5 + O(q^6), q^2 - 2*q^3 - q^4 + 2*q^5 + O(q^6) ]
TESTS:
sage: m = ModularForms(Gamma1(20),2) sage: loads(dumps(m)) == m True
Class: ModularFormsAmbient_g1_Q
self, level, weight) |
Create a space of modular forms for
of integral weight over the
rational numbers.
sage: m = ModularForms(Gamma1(100),5); m Modular Forms space of dimension 1270 for Congruence Subgroup Gamma1(100) of weight 5 over Rational Field sage: type(m) <class 'sage.modular.modform.ambient_g1.ModularFormsAmbient_g1_Q'>
Functions: cuspidal_submodule,
eisenstein_submodule
self) |
Return the cuspidal submodule of this modular forms space.
sage: m = ModularForms(Gamma1(17),2); m Modular Forms space of dimension 20 for Congruence Subgroup Gamma1(17) of weight 2 over Rational Field sage: m.cuspidal_submodule() Cuspidal subspace of dimension 5 of Modular Forms space of dimension 20 for Congruence Subgroup Gamma1(17) of weight 2 over Rational Field
self) |
Return the Eisenstein submodule of this modular forms space.
sage: ModularForms(Gamma1(13),2).eisenstein_submodule() Eisenstein subspace of dimension 11 of Modular Forms space of dimension 13 for Congruence Subgroup Gamma1(13) of weight 2 over Rational Field sage: ModularForms(Gamma1(13),10).eisenstein_submodule() Eisenstein subspace of dimension 12 of Modular Forms space of dimension 69 for Congruence Subgroup Gamma1(13) of weight 10 over Rational Field
Special Functions: __init__
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