Sparse action of Hecke operators¶
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class
sage.modular.modsym.hecke_operator.
HeckeOperator
(parent, n)¶ Bases:
sage.modular.hecke.hecke_operator.HeckeOperator
EXAMPLES:
sage: M = ModularSymbols(11) sage: H = M.hecke_operator(2005); H Hecke operator T_2005 on Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over Rational Field sage: H == loads(dumps(H)) True
We create a Hecke operator of large index (greater than 32 bits):
sage: M1 = ModularSymbols(21,2) sage: M1.hecke_operator(13^9) Hecke operator T_10604499373 on Modular Symbols space of dimension 5 for Gamma_0(21) of weight 2 with sign 0 over Rational Field
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apply_sparse
(x)¶ Return the image of
x
underself
.If
x
is not inself.domain()
, raise aTypeError
.EXAMPLES:
sage: M = ModularSymbols(17,4,-1) sage: T = M.hecke_operator(4) sage: T.apply_sparse(M.0) 64*[X^2,(1,8)] + 24*[X^2,(1,10)] - 9*[X^2,(1,13)] + 37*[X^2,(1,16)] sage: [T.apply_sparse(x) == T.hecke_module_morphism()(x) for x in M.basis()] [True, True, True, True] sage: N = ModularSymbols(17,4,1) sage: T.apply_sparse(N.0) Traceback (most recent call last): ... TypeError: x (=[X^2,(0,1)]) must be in Modular Symbols space of dimension 4 for Gamma_0(17) of weight 4 with sign -1 over Rational Field
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