parent, n) |
sage: M = ModularSymbols(11) sage: M.hecke_operator(2005) Hecke operator T_2005 on Full Modular Symbols space for Gamma_0(11) of weight 2 with sign 0 and dimension 3 over Rational Field
index,
matrix,
matrix_form
Further documentation:
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Return the index of this Hecke operator, i.e., if
this Hecke operator is
, return the int
.
sage: T = ModularSymbols(11).hecke_operator(17) sage: T.index() 17
) |
Return the matrix underlying this Hecke operator.
sage: T = ModularSymbols(11).hecke_operator(17) sage: T.matrix() [18 0 -4] [ 0 -2 0] [ 0 0 -2]
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Return the matrix form of this element of a Hecke algebra.
sage: T = ModularSymbols(11).hecke_operator(17) sage: T.matrix_form() Hecke operator on Full Modular Symbols space for Gamma_0(11) of weight 2 with sign 0 and dimension 3 over Rational Field defined by: [18 0 -4] [ 0 -2 0] [ 0 0 -2]
Instances of class HeckeOperator also have the following special methods:
__cmp__,
__mul__,
__repr__,
_latex_
Further documentation:
other) |
We create the space of modular symbols of level
and weight
, then compute
and
on it, along with their composition.
sage: M = ModularSymbols(11) sage: t2 = M.hecke_operator(2); t3 = M.hecke_operator(3) sage: t2*t3 Hecke operator T_6 on Full Modular Symbols space for Gamma_0(11) of weight 2 with sign 0 and dimension 3 over Rational Field sage: t3.matrix() * t2.matrix() [12 0 -2] [ 0 2 0] [ 0 0 2] sage: (t2*t3).matrix() [12 0 -2] [ 0 2 0] [ 0 0 2]
When we compute
the result is not (easily seen to be)
a Hecke operator of the form
, so it is returned as a
Hecke module homomorphism defined as a matrix:
sage: t2**5 Hecke operator on Full Modular Symbols space for Gamma_0(11) of weight 2 with sign 0 and dimension 3 over Rational Field defined by: [243 0 -55] [ 0 -32 0] [ 0 0 -32]
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