Modular Forms for \Gamma_1(N) over \QQ.

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: 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 sage.modular.modform.ambient_g1.ModularFormsAmbient_g1_Q(level, weight)

A space of modular forms for the group \Gamma_1(N) over the rational numbers.

__init__(level, weight)

Create a space of modular forms for \Gamma_1(N) of integral weight over the rational numbers.

EXAMPLES:

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'>
_compute_hecke_matrix(n)

Compute the matrix of the Hecke operator T_n acting on this space.

EXAMPLE:

sage: ModularForms(Gamma1(7), 4).hecke_matrix(3) # indirect doctest
[           0          -42          133            0            0            0            0            0            0]
[           0          -28           91            0            0            0            0            0            0]
[           1           -8           19            0            0            0            0            0            0]
[           0            0            0           28            0            0            0            0            0]
[           0            0            0   -10152/259            0      5222/37    -13230/37    -22295/37     92504/37]
[           0            0            0    -6087/259            0  312067/4329 1370420/4329   252805/333 3441466/4329]
[           0            0            0     -729/259            1       485/37      3402/37      5733/37      7973/37]
[           0            0            0      729/259            0      -189/37     -1404/37     -2366/37     -3348/37]
[           0            0            0      255/259            0  -18280/4329  -51947/4329   -10192/333 -190855/4329]
cuspidal_submodule()

Return the cuspidal submodule of this modular forms space.

EXAMPLES:

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
eisenstein_submodule()

Return the Eisenstein submodule of this modular forms space.

EXAMPLES:

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

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Modular Forms over a Non-minimal Base Ring

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