Factoring Hecke polynomials modulo a prime
J. Brian Conrey, David W. Farmer, Peter Jake Wallace
Abstract
Let TN,chip,k(x) be the characteristic polynomial of the Hecke operator Tp acting on the space of cusp forms Sk(N,chi). We describe the factorization of TN,chip,k(x) mod l as k varies, and we explicitly calculate those factorizations for N=1 and small l. These factorizations are used to deduce the irreducibility of certain T1,1q,k(x) from the irreducibility of T1,12,k(x).
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