Hecke algebra (awaiting review)

For a commutative ring $R$ and an $R$-module $M$ equipped with an action of Hecke operators, such as spaces of modular forms or modular symbols, the associated $R$-Hecke algebra is the $R$-subalgebra of the $R$-endomorphism ring of $M$ generated by the Hecke operators.

We usually include all Hecke operators, i.e. also those the index of which divides the level or is a multiple of the characteristic (if applicable).

If the ring $R$ is not mentioned, then it is either $\Q$ or $\C$, depending on the context.