{
  "id": "1110.6430",
  "version": "v1",
  "published": "2011-10-28T19:31:10.000Z",
  "updated": "2011-10-28T19:31:10.000Z",
  "title": "Hecke Eigenforms as Products of Eigenforms",
  "authors": [
    "Matthew L. Johnson"
  ],
  "comment": "26 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate when the product of two Hecke eigenforms for {\\Gamma}_1(N) is again a Hecke eigenform. In this paper we prove that the product of two normalized eigenforms for {\\Gamma}_1(N), of weight greater than 1, is an eigenform only 61 times, and give a complete list. Duke [Duk99] and Ghate [Gha00] independently proved that with eigenforms for SL_2(Z), there are only 16 such product identities. Ghate [Gha02] also proved related results for {\\Gamma}_1(N), with N square free. Emmons [Emm05] proved results for eigenforms away from the level, for prime level. The methods we use are elementary and effective, and do not rely on the Rankin-Selberg convolution method used by both Duke and Ghate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-28T19:31:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hecke eigenform",
      "rankin-selberg convolution method",
      "weight greater",
      "prime level",
      "eigenforms away"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6430J"
    }
  }
}