{
  "id": "0903.3201",
  "version": "v2",
  "published": "2009-03-18T16:54:55.000Z",
  "updated": "2009-08-02T21:47:19.000Z",
  "title": "Cohomology of Congruence Subgroups of SL_4(Z). III",
  "authors": [
    "Avner Ash",
    "Paul E. Gunnells",
    "Mark McConnell"
  ],
  "comment": "incorporates referees' comments",
  "categories": [
    "math.NT",
    "math.NA"
  ],
  "abstract": "In two previous papers [AGM1, AGM2] we computed cohomology groups H^5(\\Gamma_0 (N); \\C) for a range of levels N, where \\Gamma_0 (N) is the congruence subgroup of SL_4 (\\Z) consisting of all matrices with bottom row congruent to (0,0,0,*) mod N. In this note we update this earlier work by carrying it out for prime levels up to N = 211. This requires new methods in sparse matrix reduction, which are the main focus of the paper. Our computations involve matrices with up to 20 million non-zero entries. We also make two conjectures concerning the contributions to H^5(\\Gamma_0 (N); \\C) for N prime coming from Eisenstein series and Siegel modular forms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-02T21:47:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F75",
      "65F05",
      "65F50"
    ],
    "keywords": [
      "congruence subgroup",
      "sparse matrix reduction",
      "siegel modular forms",
      "million non-zero entries",
      "row congruent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.3201A"
    }
  }
}