{
  "id": "1805.09373",
  "version": "v1",
  "published": "2018-05-23T18:41:40.000Z",
  "updated": "2018-05-23T18:41:40.000Z",
  "title": "On the cohomology of congruence subgroups of GL3 over the Eisenstein integers",
  "authors": [
    "Paul E. Gunnells",
    "Mark McConnell",
    "Dan Yasaki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be the congruence subgroup of level n consisting of matrices with bottom row (0,0,*) bmod n. In this paper we compute the cohomology spaces H^{nu - 1} (Gamma_0 (n); C) as a Hecke module for various levels n, where nu is the virtual cohomological dimension of Gamma. This represents the first attempt at such computations for GL_3 over an imaginary quadratic field, and complements work of Grunewald--Helling--Mennicke and Cremona, who computed the cohomology of GL_2 over imaginary quadratic fields. In our results we observe a variety of phenomena, including cohomology classes that apparently correspond to nonselfdual cuspforms on GL_3/F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T18:41:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "11F67",
      "11G05",
      "11Y99"
    ],
    "keywords": [
      "congruence subgroup",
      "imaginary quadratic field",
      "eisenstein integers",
      "nonselfdual cuspforms",
      "cohomology spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}