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On the eigenvalues of Hecke operators

✍ Scribed by Andrew P. Ogg


Publisher
Springer
Year
1969
Tongue
English
Weight
360 KB
Volume
179
Category
Article
ISSN
0025-5831

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Let K be the splitting field of the characteristic polynomial of the Hecke operator T 2 acting on the d-dimensional space of cusp forms of weight k and level 1. We show, for various values of k, that the Galois group Gal(KΓ‚Q) is the full symmetric group on d symbols.

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We use the action of the Hecke operators T j (p 2 ) (1 j n) on the Fourier coefficients of Siegel modular forms to bound the eigenvalues of these Hecke operators. This extends work of Duke-Howe-Li and of Kohnen, who provided bounds on the eigenvalues of the operator T (p).