{
  "id": "2307.07804",
  "version": "v1",
  "published": "2023-07-15T13:37:56.000Z",
  "updated": "2023-07-15T13:37:56.000Z",
  "title": "Eigenspaces of Newforms with Nontrivial Character",
  "authors": [
    "Markos Karameris"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $S_{k}(\\Gamma_0(N),\\chi)$ denote the space of holomorphic cuspforms with Dirichlet character $\\chi$ and modular subgroup $\\Gamma_0(N)$. We will characterize the space of newforms $S_{k}^{new}(\\Gamma_0(N),\\chi)$ as the intersection of eigenspaces of a particular family of Hecke operators, generalizing the work of Baruch-Purkait to forms with non-trivial character. We achieve this by obtaining representation theoretic results in the $p$-adic case which we then de-adelizize into relations of classical operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-15T13:37:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F33",
      "20C08",
      "11F25"
    ],
    "keywords": [
      "nontrivial character",
      "eigenspaces",
      "obtaining representation theoretic results",
      "modular subgroup",
      "hecke operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}