M) |
INPUT: M -- a Hecke module
basis,
discriminant,
gen,
gens,
hecke_matrix,
hecke_operator,
is_noetherian,
level,
module,
ngens,
rank
Further documentation:
n) |
Return the
-th Hecke operator.
sage: T = ModularSymbols(11).hecke_algebra() sage: T.gen(2) Hecke operator T_2 on Full Modular Symbols space for Gamma_0(11) of weight 2 with sign 0 and dimension 3 over Rational Field
) |
Return a generator over all Hecke operator
for
. This is infinite.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: g = T.gens() sage: g.next() Hecke operator T_1 on Full Modular Symbols space for Gamma_0(1) of weight 12 with sign 0 and dimension 3 over Rational Field sage: g.next() Hecke operator T_2 on Full Modular Symbols space for Gamma_0(1) of weight 12 with sign 0 and dimension 3 over Rational Field
n) |
Return the matrix of the n-th Hecke operator
.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.hecke_matrix(2) [ -24 0 0] [ 0 -24 0] [4860 0 2049]
n) |
Return the n-th Hecke operator
.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.hecke_operator(2) Hecke operator T_2 on Full Modular Symbols space for Gamma_0(1) of weight 12 with sign 0 and dimension 3 over Rational Field
) |
Return True if this Hecke algebra is Noetherian as a ring.
) |
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.module() Full Modular Symbols space for Gamma_0(1) of weight 12 with sign 0 and dimension 3 over Rational Field
Instances of class HeckeAlgebra_base also have the following special methods:
__call__,
__contains__,
__repr__,
_HeckeAlgebra_base__matrix_space,
_latex_
Further documentation:
x) |
sage: T = ModularSymbols(11).hecke_algebra() sage: T.gen(2) in T True sage: 5 in T False
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