Cohomology of congruence subgroups of SL4(ℤ)1

Avner Ash; Paul E. Gunnells; Mark McConnell

doi:10.1006/jnth.2001.2730

Cohomology of congruence subgroups of SL₄(ℤ)¹

Avner Ash, Paul E. Gunnells, Mark McConnell

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let N > 1 be an integer, and let Γ = Γ₀(N) ⊂ SL₄ (ℤ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H⁵(Γ; ℂ) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.

Original language	English (US)
Pages (from-to)	181-212
Number of pages	32
Journal	Journal of Number Theory
Volume	94
Issue number	1
DOIs	https://doi.org/10.1006/jnth.2001.2730
State	Published - 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Keywords

Cohomology of arithmetic groups
Hecke operators
Modular symbols

Access to Document

10.1006/jnth.2001.2730

Cite this

@article{1191643aca544dfeae22c9dcfa9bd3aa,

title = "Cohomology of congruence subgroups of SL4(ℤ)1",

abstract = "Let N > 1 be an integer, and let Γ = Γ0(N) ⊂ SL4 (ℤ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; ℂ) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.",

keywords = "Cohomology of arithmetic groups, Hecke operators, Modular symbols",

author = "Avner Ash and Gunnells, {Paul E.} and Mark McConnell",

note = "Funding Information: 1The research of the first author was partially supported by NSF Grant DMS-9531675. The second author was partially supported by a Columbia University Faculty Research grant and NSF Grant DMS-9627870. The third author was partially supported by NSF Grant DMS-9704535. We thank Eric Conrad for some assistance with programming, and Peter Woit for excellent computing support. We thank David Ginzburg for conversations at the beginning of this project.",

year = "2002",

doi = "10.1006/jnth.2001.2730",

language = "English (US)",

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pages = "181--212",

journal = "Journal of Number Theory",

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T1 - Cohomology of congruence subgroups of SL4(ℤ)1

AU - Ash, Avner

AU - Gunnells, Paul E.

AU - McConnell, Mark

N1 - Funding Information: 1The research of the first author was partially supported by NSF Grant DMS-9531675. The second author was partially supported by a Columbia University Faculty Research grant and NSF Grant DMS-9627870. The third author was partially supported by NSF Grant DMS-9704535. We thank Eric Conrad for some assistance with programming, and Peter Woit for excellent computing support. We thank David Ginzburg for conversations at the beginning of this project.

PY - 2002

Y1 - 2002

N2 - Let N > 1 be an integer, and let Γ = Γ0(N) ⊂ SL4 (ℤ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; ℂ) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.

AB - Let N > 1 be an integer, and let Γ = Γ0(N) ⊂ SL4 (ℤ) be the subgroup of matrices with bottom row congruent to (0, 0, 0, *) modN. We compute H5(Γ; ℂ) for a range of N and compute the action of some Hecke operators on many of these groups. We relate the classes we find to classes coming from the boundary of the Borel-Serre compactification, to Eisenstein series, and to classical holomorphic modular forms of weights 2 and 4.

KW - Cohomology of arithmetic groups

KW - Hecke operators

KW - Modular symbols

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