{
  "id": "1905.10036",
  "version": "v1",
  "published": "2019-05-24T05:10:06.000Z",
  "updated": "2019-05-24T05:10:06.000Z",
  "title": "Realization of Modular Galois Representations in Jacobians of modular curves",
  "authors": [
    "Peng Tian"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we propose an improved algorithm for computing mod $\\ell$ Galois representations associated to eigenforms of arbitrary levels prime to $\\ell$. Precisely, we present a method to find the Jacobians of modular curves which have the smallest possible dimensions in a well-defined sense to realize the modular Galois representations. This algorithm also works without the assumption $\\ell \\ge k-1$, where $k$ are the weights of the eigenforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-24T05:10:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "modular galois representations",
      "modular curves",
      "realization",
      "arbitrary levels prime",
      "eigenforms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}