The irreducibility of some level 1 Hecke polynomials

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 over Q for k 2000 and p < 2000, p prime.

• Type: Journal
• Year: 2002
• Where: MOC
• Authors: D. W. Farmer, K. James
• Keywords: Characteristic Polynomial, Cusp Forms, Hecke Operator Tp, MOC 2002