A Hecke module is a module
over the anemic Hecke
algebra, i.e., the Hecke algebra generated by Hecke operators
with
coprime to the level of
. (Every Hecke module
defines a level function, which is a positive integer.) The
reason we require that
only be a module over the anemic Hecke
algebra is that many natural maps, e.g., degeneracy maps,
Atkin-Lehner operators, etc., are
-module homomorphisms; but
they are homomorphisms over the anemic Hecke algebra.
We create the category of Hecke modules over
.
sage: C = HeckeModules(RationalField()); C Category of Hecke modules over Rational Field
Note that the base ring can be an arbitrary commutative ring.
sage: HeckeModules(IntegerRing()) Category of Hecke modules over Integer Ring sage: HeckeModules(FiniteField(5)) Category of Hecke modules over Finite field of size 5
The base ring doesn't have to be a principal ideal domain.
sage: HeckeModules(PolynomialRing(IntegerRing())) Category of Hecke modules over Univariate Polynomial Ring in x over Integer Ring
R) |
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