Computing Hecke eigenvalues below the cohomological dimension

Details Computing Hecke eigenvalues below the cohomological dimension Computing Hecke eigenvalues below the cohomological dimension

1998-11-23

arxiv.org/abs/math/9811134v2

Mathematics

Number Theory

26 pages, 12 figures, uses psfrag.sty, incorporates referree's changes

Scientific paper

Let G be a torsion-free finite-index subgroup of SL(n,Z) or GL(n,Z), and let d be the cohomological dimension of G. We present an algorithm to compute the eigenvalues of the Hecke operators on the integral cohomology of degree d-1 for n = 2, 3, and 4. In addition, we describe a modification of the modular symbol algorithm of Ash-Rudolph for computing Hecke eigenvalues for the integral cohomology of degree d.

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