Conjectures about Discriminants of Hecke Algebras of Prime Level

摘要

In this paper, we study p-divisibility of discriminants 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 precise conjecture about indexes of Hecke algebras in their normalisation which implies (if true) the surprising conjecture that there are no mod p congruences between non-conjugate newforms in S_2(Γ_0(p)), but there are almost always many such congruences when the weight is bigger than 2.