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>