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Hecke eigenforms in the cohomology of congruence subgroups of \(\operatorname{SL}(3,\mathbb Z)\). (English) Zbl 1088.11037

Summary: We list here Hecke eigenvalues of several automorphic forms for congruence subgroups of \(\text{SL}(3,\mathbb Z)\). To compute such tables, we describe an algorithm that combines techniques developed by Ash, Grayson and Green with the Lenstra-Lenstra-Lovász algorithm. With our implementation of this new algorithm we are able to handle much larger levels than those treated by Ash, Grayson and Green and by Top and van Geemen in previous work. Comparing our tables with results form computations of Galois representations, we find some new numerical evidence for the conjectured relation between modular forms and Galois representations.

MSC:

11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F75 Cohomology of arithmetic groups
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References:

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