Contents Online
Mathematical Research Letters
Volume 10 (2003)
Number 5
Irreducibility of Hecke polynomials
Pages: 709 – 715
DOI: https://dx.doi.org/10.4310/MRL.2003.v10.n5.a13
Authors
Abstract
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 $p$.
Published 1 January 2003