Full p-adic Hecke Algebra

A full -adic Hecke algebra at level , with not dividing , combines the Hecke actions on holomorphic modular forms of all positive integer weights. Let be the -algebra acting on generated by and for primes not dividing . Here includes Eisenstein forms, and on weight the operator is times the diamond operator. The full algebra is

Its topology is the inverse-limit topology of the -adic topologies at finite weight cutoffs.