Let Tp,k(x) be the characteristic polynomial of the Hecke operator Tp acting on the space of level 1 cusp forms Sk(1). We show that Tp,k(x) is irreducible and has full Galois group...
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 a...