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Computing Hecke eigenvalues below the cohomological dimension

Paul E. Gunnells
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Abstract

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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Paul E. Gunnells. 1999-10-20. Computing Hecke eigenvalues below the cohomological dimension. https://arxiv.org/abs/math/9811134

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