Mathematical Research Letters

Volume 10, Issue 5, September 2003 pp. 709-715.

Irreducibility of Hecke polynomials

Authors: Srinath Baba and M. Ram Murty
Author institution: Max Planck Institut für Mathematik, and Queen's University

Summary: 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 $p$.

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