{
  "id": "1109.2251",
  "version": "v2",
  "published": "2011-09-10T19:07:34.000Z",
  "updated": "2013-11-28T15:12:18.000Z",
  "title": "A space of weight one modular forms attached to totally real cubic number fields",
  "authors": [
    "Guillermo Mantilla-Soler"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $d$ be a positive fundamental discriminant, and let $\\mathcal{C}_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$. For each $K \\in \\mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with level $3^{\\pm 1}d$ and nebentypus $\\left( \\frac{-3^{\\pm 1}d}{\\cdot} \\right)$. We show that the form $f_{K}$ completely determines the field $K$. Moreover, we show that $\\{f_{K} : K \\in \\mathcal{C}_{d}\\}$ is a linearly independent set.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-28T15:12:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R16",
      "11F27"
    ],
    "keywords": [
      "totally real cubic number fields",
      "modular forms",
      "positive fundamental discriminant",
      "linearly independent set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.2251M"
    }
  }
}