Conjectures about discriminants of Hecke algebras at prime level

2004/06/11 by Calegari, Frank, Stein, William
#11G05 #11G10 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0406243

Abstract

We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture that there are no mod p congruences between non-conjugate newforms of weight 2 and level Gamma₀(p).

Related

• On mod p representations which are defined over F_p: II
• On Drinfeld cusp forms of prime level
• The Hecke Algebra T_k has Large Index
• Hecke algebras, new vectors and new forms on Γ₀(m)
• Indices of nilpotency in certain spaces of modular forms