{
  "id": "1901.02115",
  "version": "v1",
  "published": "2019-01-08T00:51:31.000Z",
  "updated": "2019-01-08T00:51:31.000Z",
  "title": "Paramodular forms coming from elliptic curves",
  "authors": [
    "Manami Roy"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "There is a lifting from a non-CM elliptic curve $E/\\mathbb{Q}$ to a paramodular form $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find the level of $f$ in an explicit way in terms of the coefficients of the Weierstrass equation of $E$. In order to compute the paramodular level, we use the available description of the local representations of $\\mathrm{GL}(2,\\mathbb{Q}_p)$ attached to $E$ for $p \\ge 5$ and determine the local representation of $\\mathrm{GL}(2,\\mathbb{Q}_3)$ attached to $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-08T00:51:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F46",
      "11G07"
    ],
    "keywords": [
      "paramodular forms coming",
      "local representation",
      "non-cm elliptic curve",
      "symmetric cube map",
      "paramodular level"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}