Computing Heeke Eigenvalues Below the Cohomologieal Dimension
- 1 January 2000
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 9 (3) , 351-367
- https://doi.org/10.1080/10586458.2000.10504412
Abstract
Let Γ be a torsion-free finite-index subgroup of SLn(Z) or GLn(Z), and let υ be the cohomological dimension of Γ. We present an algorithm to compute the eigenvalues of the Hecke operators on Hυ–1(Γ; 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 Hυ(Γ; Z).Keywords
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This publication has 24 references indexed in Scilit:
- Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted CoefficientsExperimental Mathematics, 1998
- Unstable Cohomology of SL(n,O)Journal of Algebra, 1994
- A Course in Computational Algebraic Number TheoryPublished by Springer Nature ,1993
- Galois representations attached to modp cohomology of GL(n,ℤ)Duke Mathematical Journal, 1992
- Experimental Indications of Three-dimensional Galois Representations from the Cohomology of SL(3, Z)Experimental Mathematics, 1992
- An $$\widehat{A_4 }$$ extension of ? attached to a non-selfdual automorphic form onGL(3)Mathematische Annalen, 1991
- Computations of cuspidal cohomology of congruence subgroups of SL(3, Z)Journal of Number Theory, 1984
- The modular symbol and continued fractions in higher dimensionsInventiones Mathematicae, 1979
- Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous conesMathematische Annalen, 1977
- Corners and arithmetic groupsCommentarii Mathematici Helvetici, 1973