{
  "id": "1703.08145",
  "version": "v1",
  "published": "2017-03-23T17:09:56.000Z",
  "updated": "2017-03-23T17:09:56.000Z",
  "title": "Weakly holomorphic modular forms in prime power levels of genus zero",
  "authors": [
    "Paul Jenkins",
    "DJ Thornton"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $M_k^\\sharp(N)$ be the space of weight $k$, level $N$ weakly holomorphic modular forms with poles only at the cusp at $\\infty$. We explicitly construct a canonical basis for $M_k^\\sharp(N)$ for $N\\in\\{8,9,16,25\\}$, and show that many of the Fourier coefficients of the basis elements in $M_0^\\sharp(N)$ are divisible by high powers of the prime dividing the level $N$. Additionally, we show that these basis elements satisfy a Zagier duality property, and extend Griffin's results on congruences in level 1 to levels 2, 3, 4, 5, 7, 8, 9, 16, and 25.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-23T17:09:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F37",
      "11F33"
    ],
    "keywords": [
      "weakly holomorphic modular forms",
      "prime power levels",
      "genus zero",
      "extend griffins results",
      "basis elements satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}