Discriminants of Hecke Algebras at Prime Level

William A. Stein¹

Date: September 24, 2002

Abstract:

We study $p$-divisibility of discriminant of Hecke algebras associated to spaces of cusp forms of prime level. By considering cusp forms of weight bigger than $2$, we are are led to make a conjecture about indexes of Hecke algebras in their normalization which, if true, implies that there are no mod $p$ congruences between non-conjugate newforms in $S_2(\Gamma_0(p))$.