{
  "id": "1611.08969",
  "version": "v1",
  "published": "2016-11-28T03:13:21.000Z",
  "updated": "2016-11-28T03:13:21.000Z",
  "title": "Counting Eta-Quotients of Prime Level",
  "authors": [
    "Allison Arnold-Roksandich",
    "Kevin James",
    "Rodney Keaton"
  ],
  "comment": "13 pages, 3 tables, REU results",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is known that all modular forms on SL_2(Z) can be expressed as a rational function in eta(z), eta(2z) and eta(4z). By utilizing known theorems, and calculating the order of vanishing, we can compute the eta-quotients for a given level. Using this count, knowing how many eta-quotients are linearly independent and using the dimension formula, we can figure out a subspace spanned by the eta-quotients. In this paper, we primarily focus on the case where N=p a prime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T03:13:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F20",
      "11F11",
      "11F37"
    ],
    "keywords": [
      "prime level",
      "counting eta-quotients",
      "modular forms",
      "rational function",
      "dimension formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}