{
  "id": "1309.3717",
  "version": "v3",
  "published": "2013-09-15T01:38:14.000Z",
  "updated": "2016-04-01T13:35:56.000Z",
  "title": "On the modularity of reducible mod l Galois representations",
  "authors": [
    "Nicolas Billerey",
    "Ricardo Menares"
  ],
  "comment": "Minor modifications. Accepted for publication in Mathematical Research Letters",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We prove that every odd semisimple reducible (2-dimensional) mod l Galois representation arises from a cuspidal eigenform. In addition, we investigate the possible different types (level, weight, character) of such a modular form. When the representation is the direct sum of the trivial character and a power of the mod l cyclotomic character, we are able to characterize the primes that can arise as levels of the associated newforms. As an application, we determine a new explicit lower bound for the highest degree among the fields of coefficients of newforms of trivial Nebentypus and prime level. The bound is valid in a subset of the primes with natural (lower) density at least one half.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-01T02:03:13.000Z",
      "comment": "added references, minor wording modifications",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-04-01T13:35:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F80",
      "11F33",
      "11N25"
    ],
    "keywords": [
      "reducible mod",
      "modularity",
      "explicit lower bound",
      "galois representation arises",
      "highest degree"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3717B"
    }
  }
}