Irreducibility of Hecke polynomials

In this note, we show that if the characteristic polynomial of some Hecke operator $T_n$ acting on the space of weight $k$ cusp forms for the group $\hbox{SL}_2(\Bbb Z)$ is irreducible, then the same holds for $T_p$, where $p$ runs through a density one set of primes. This proves that if Maeda’s conjecture is true for some $T_n$, then it is true for $T_p$ for almost all primes $p$.

Full Text (PDF format)

Published 1 January 2003