{
  "id": "0811.2259",
  "version": "v2",
  "published": "2008-11-14T03:18:48.000Z",
  "updated": "2009-07-22T08:22:29.000Z",
  "title": "Modular Forms of weight 8 for $Γ_g(1,2)$",
  "authors": [
    "M. Oura",
    "C. Poor",
    "R. Salvati Manni",
    "D. Yuen"
  ],
  "comment": "accepted for publication in Math.Ann",
  "categories": [
    "math.NT",
    "hep-th"
  ],
  "abstract": "We complete the program indicated by the Ansatz of D'Hoker and Phong in genus ~4 by proving the uniqueness of the restriction to Jacobians of the weight 8 Siegel cusp forms satisfying the Anstaz. We prove $\\dim [\\Gamma_4(1,2),8]_0=2$ and $\\dim [\\Gamma_4(1,2),8]=7$. In each genus, we classify the linear relations among the self-dual lattices of rank {16}. We extend the program to genus ~5 by constructing the unique linear combination of theta series that satisfies the Ansatz.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-22T08:22:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular forms",
      "unique linear combination",
      "siegel cusp forms satisfying",
      "theta series",
      "linear relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.2259O"
    }
  }
}