{
  "id": "1706.07885",
  "version": "v1",
  "published": "2017-06-23T23:53:53.000Z",
  "updated": "2017-06-23T23:53:53.000Z",
  "title": "Periods of modular forms on $Γ_0(N)$ and products of Jacobi theta functions",
  "authors": [
    "Y. Choie",
    "Y. Park",
    "D. Zagier"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Generalizing a result of~\\cite{Z1991} for modular forms of level~one, we give a closed formula for the sum of all Hecke eigenforms on $\\Gamma_0(N)$, multiplied by their odd period polynomials in two variables, as a single product of Jacobi theta series for any squarefree level $N$. We also show that for $N=2$,~3 and~5 this formula completely determines the Fourier expansions of all Hecke eigenforms of all weights on $\\Gamma_0(N)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-23T23:53:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F67",
      "11F12",
      "11F25",
      "11F50"
    ],
    "keywords": [
      "jacobi theta functions",
      "modular forms",
      "hecke eigenforms",
      "odd period polynomials",
      "jacobi theta series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}