Factoring Hecke polynomials modulo a prime

J. Brian Conrey, David W. Farmer, Peter Jake Wallace

Let T^{N,chi}_{p,k}(x) be the characteristic polynomial of the Hecke operator T_p acting on the space of cusp forms S_k(N,chi). We describe the factorization of T^{N,chi}_{p,k}(x)…