Mathematical Research Letters

Volume 10 (2003)

Number 5

Irreducibility of Hecke polynomials

Pages: 709 – 715



Srinath Baba (Max Planck Institut für Mathematik)

M. Ram Murty (Queen’s University)


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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