Some non-Gorenstein Hecke algebras attached to spaces of modular forms

Abstract

Let p be a prime, and let S2 (Γ0 (p)) be the space of cusp forms of level Γ0 (p) and weight 2. We prove that, for p ε {431, 503, 2089}, there exists a non-Eisenstein maximal ideal m of the Hecke algebra of S2(Γ0(p)) above 2, such that (Tq)m is not Gorenstein. © 2002 Elsevier Science (USA).