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2000 Computing Hecke eigenvalues below the cohomological dimension
Paul E. Gunnells
Experiment. Math. 9(3): 351-367 (2000).

Abstract

Let $\funnyGamma$ be a torsion-free finite-index subgroup of $\SL_{n} (\Z )$ or $\GL_{n} (\Z )$, and let $\nu $ be the cohomological dimension of $\funnyGamma $. We present an algorithm to compute the eigenvalues of the Hecke operators on $H^{\nu -1} (\funnyGamma ;\Z )$, for n= 2, 3, and 4. In addition, we describe a modification of the modular symbol algorithm of Ash and Rudolph for computing Hecke eigenvalues on $H^{\nu } (\funnyGamma ;\Z )$.

Citation

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Paul E. Gunnells. "Computing Hecke eigenvalues below the cohomological dimension." Experiment. Math. 9 (3) 351 - 367, 2000.

Information

Published: 2000
First available in Project Euclid: 18 February 2003

zbMATH: 1037.11037
MathSciNet: MR1795307

Subjects:
Primary: 11F67 , 11F75 , 11H55 , 11Y16

Keywords: $LLL$-reduction , automorphic forms , cohomology of arithemetic groups , Hecke operators , modular symbols , sharbly complex , Voronoi-reduction

Rights: Copyright © 2000 A K Peters, Ltd.

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