The irreducibility of some level 1 Hecke polynomials

Farmer, D.; James, K.

doi:10.1090/S0025-5718-01-01375-8

The irreducibility of some level 1 Hecke polynomials
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by D. W. Farmer and K. James;

Math. Comp. 71 (2002), 1263-1270

DOI: https://doi.org/10.1090/S0025-5718-01-01375-8

Published electronically: June 22, 2001

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Abstract:

Let $T_{p,k}(x)$ be the characteristic polynomial of the Hecke operator $T_{p}$ acting on the space of level 1 cusp forms $S_{k}(1)$. We show that $T_{p,k}(x)$ is irreducible and has full Galois group over $\mathbf {Q}$ for $k\le 2000$ and $p<2000$, $p$ prime.

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