{
  "id": "1108.4619",
  "version": "v1",
  "published": "2011-08-23T14:50:02.000Z",
  "updated": "2011-08-23T14:50:02.000Z",
  "title": "Weight reduction for cohomological mod $p$ modular forms over imaginary quadratic fields",
  "authors": [
    "Adam Mohamed"
  ],
  "comment": "30 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ F$ be an imaginary quadratic field and $\\mathcal{O}$ its ring of integers. Let $ \\mathfrak{n} \\subset \\mathcal{O} $ be a non-zero ideal and let $ p> 5$ be a rational inert prime in $F$ and coprime with $\\mathfrak{n}$. Let $ V$ be an irreducible finite dimensional representation of $ \\bar{\\mathbb{F}}_{p}[{\\rm GL}_2(\\mathbb{F}_{p^2})].$ We establish that a system of Hecke eigenvalues appearing in the cohomology with coefficients in $ V$ already lives in the cohomology with coefficients in $ \\bar{\\mathbb{F}}_{p}\\otimes det^e$ for some $ e \\geq 0$; except possibly in some few cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-23T14:50:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic field",
      "weight reduction",
      "modular forms",
      "cohomological mod",
      "irreducible finite dimensional representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.4619M"
    }
  }
}