{
  "id": "1701.07864",
  "version": "v1",
  "published": "2017-01-26T20:15:23.000Z",
  "updated": "2017-01-26T20:15:23.000Z",
  "title": "Congruences for modular forms mod 2 and quaternionic $S$-ideal classes",
  "authors": [
    "Kimball Martin"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove many simultaneous congruences mod 2 for elliptic and Hilbert modular forms among forms with different Atkin--Lehner eigenvalues. The proofs involve the notion of quaternionic $S$-ideal classes and the distribution of Atkin--Lehner signs among newforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-26T20:15:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular forms mod",
      "ideal classes",
      "quaternionic",
      "hilbert modular forms",
      "simultaneous congruences mod"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}