Computations of cuspidal cohomology of congruence subgroups of SL(3,\({\mathbb{Z}})\)

DOI10.1016/0022-314X(84)90081-7zbMath0552.10015MaRDI QIDQ800957

Philip Green, Avner Ash, Daniel R. Grayson

Publication date: 1984

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

tablesdimensionexplicit computationscongruence groupsarithmetic quotientcusp cohomologyaction of the Hecke algebraeigenvalues of Hecke operatorsexplicit algorithms

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Theta series; Weil representation; theta correspondences (11F27) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Algorithms in computer science (68W99)

Related Items

Computing Heeke Eigenvalues Below the Cohomologieal Dimension, Experimental Indications of Three-dimensional Galois Representations from the Cohomology of SL(3, Z), A non-selfdual automorphic representation of \(\text{GL}_3\) and a Galois representation, Cohomology at infinity and the well-rounded retract for general linear groups, Cohomology of congruence subgroups of \(\mathrm{SL}_3(\mathbb{Z})\), Steinberg modules, and real quadratic fields, EVERYWHERE UNRAMIFIED AUTOMORPHIC COHOMOLOGY FOR SL₃(ℤ), Hecke Operators and Hilbert Modular Forms, Heeke Eigenforms in the Cohomology of Congruence Subgroups of SL(3, Z), Galois representations attached to mod \(p\) cohomology of \(GL(n,\mathbb{Z})\), An explicit spine for the Picard modular group over the Gaussian integers, On the \(\mathrm {GL}_n\)-eigenvariety and a conjecture of Venkatesh, Unnamed Item, On the Cohomology of Congruence Subgroups of GL₃ over the Eisenstein Integers, An \(\widehat{A_4}\) extension of \({\mathbb{Q}}\) attached to a non-selfdual automorphic form on \(GL(3)\), Vanishing of the cuspidal cohomology of congruence subgroups of \(\text{GL}_ n(\mathbb{Z})\), Cohomology of congruence subgroups of \(\text{SL}(4,\mathbb Z)\). II, Lectures on Computing Cohomology of Arithmetic Groups, Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients

Cites Work

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• On the top betti number of subgroups of \(SL(n,Z)\)
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• Connection of the dual space of a group with the structure of its closed subgroups
• Cohomology of arithmetic subgroups of SL3 at infinity.
• A relation between automorphic forms on GL (2) and GL (3)
• A table of Hecke operators, II