{
  "id": "1811.00397",
  "version": "v1",
  "published": "2018-11-01T14:09:12.000Z",
  "updated": "2018-11-01T14:09:12.000Z",
  "title": "A note on cusp forms and representations of $\\mathrm{SL}_2(\\mathbb{F}_p)$",
  "authors": [
    "Zhe Chen"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Cusp forms are certain holomorphic functions defined on the upper half-plane, and the space of cusp forms for the principal congruence subgroup $\\Gamma(p)$, $p$ a prime, is acted by $\\mathrm{SL}_2(\\mathbb{F}_p)$. Meanwhile, there is a finite field incarnation of the upper half-plane, the Deligne--Lusztig (or Drinfeld) curve, whose cohomology space is also acted by $\\mathrm{SL}_2(\\mathbb{F}_p)$. In this note we study the relation between these two spaces in the weight $2$ case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-01T14:09:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cusp forms",
      "representations",
      "upper half-plane",
      "finite field incarnation",
      "principal congruence subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}