On the Cohomology of Congruence Subgroups of GL3 over the Eisenstein Integers

Paul E. Gunnells, Mark McConnell, Dan Yasaki

Research output: Contribution to journalArticle

Abstract

Let F be the imaginary quadratic field of discriminant −3 and (Formula presented.) its ring of integers. Let Γ be the arithmetic group (Formula presented.) and for any ideal (Formula presented.) let (Formula presented.) be the congruence subgroup of level (Formula presented.) consisting of matrices with bottom row (Formula presented.) In this paper we compute the cohomology spaces (Formula presented.) as a Hecke module for various levels (Formula presented.) where ν is the virtual cohomological dimension of Γ. This represents the first attempt at such computations for GL3 over an imaginary quadratic field, and complements work of Grunewald–Helling–Mennicke and Cremona, who computed the cohomology of (Formula presented.) over imaginary quadratic fields. In our results we observe a variety of phenomena, including cohomology classes that apparently correspond to nonselfdual cuspforms on (Formula presented.).

Original languageEnglish (US)
JournalExperimental Mathematics
DOIs
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • automorphic forms
  • cohomology of arithmetic groups
  • computational number theory

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