{
  "id": "math/0702545",
  "version": "v2",
  "published": "2007-02-19T12:12:26.000Z",
  "updated": "2008-02-29T06:42:07.000Z",
  "title": "On the maps from X(4p) to X(4)",
  "authors": [
    "Samar Jaafar",
    "Kamal Khuri-Makdisi"
  ],
  "comment": "12 pages, minor revisions following referee's report",
  "journal": "International Journal of Number Theory 5 (2009), no. 5, 831-844",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study pullbacks of modular forms of weight 1 from the modular curve X(4) to the modular curve X(4p), where p is an odd prime. We find the extent to which such modular forms separate points on X(4p). Our main result is that these modular forms give rise to a morphism F from the quotient of X(4p) by a certain involution i to projective space, such that F is a projective embedding of X(4p)/i away from the cusps. We also report on computer calculations regarding products of such modular forms, going up to weight 4 for p <= 13, and up to weight 3 for p <= 23, and make a conjecture about these products and about the nature of the singularities at the cusps of the image F(X(4p)/i).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-29T06:42:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F23"
    ],
    "keywords": [
      "modular forms separate points",
      "modular curve",
      "computer calculations regarding products",
      "odd prime",
      "study pullbacks"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2545J"
    }
  }
}