Hecke eigenforms in the Cuspidal Cohomology of Congruence Subgroups of SL(3,Z), by Bert van Geemen, Wilberd van der Kallen, Jaap Top, Alain Verberkmoes

This paper has appeared in Experimental Math, Volume 6, no. 2 (1997), 163-174, and so the dvi version has been removed. This paper describes an algorithm for computing with the cohomology of congruence subgroups of SL(3,Z). Basically, the algorithm combines techniques developed by Ash, Grayson and green with the LLL lattice reduction algorithm. This results in some tables of eigenvalues of Hecke operators, and two examples in the spirit of an earlier paper of two of the authors (Invent. Math. 117 (1994)) providing numerical evidence to conjectures of Langlands and of Clozel.

Bert van Geemen, Wilberd van der Kallen, Jaap Top, Alain Verberkmoes <J.Top@math.rug.nl>