{
  "abstract": "In this article, we first prove that the Hecke operator $T_t$ has no eigenform in $\\Sla$ with eigenvalue $-t^{k/2}$, when the characteristic of the base field is odd. Furthermore, if $\\dim \\Slt$ is even, we show that $T_t$ has no eigenform in $\\Sla$ with eigenvalue $t^{k/2}$. As a consequence, we prove that the direct sum decomposition $\\Slt=\\Sold \\oplus \\Snew$ holds when $\\dim \\Slt$ is even. This proves the conjecture \\cite[Conjecture 1.1(3)]{BV19a} of Bandini and Valentino for an infinite family of cusp forms. In particular, for any weight $k$, there exists at least one type $m$ (there are only two possible non-trivial values of $m$) for which the conjecture \\cite[Conjecture 1.1(3)]{BV19a} is true.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14167",
  "author_total": 1,
  "authors": [
    {
      "name": "Tarun Dalal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bwp7ndqbh5bqh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14167",
  "fulltext_url": null,
  "id": "bwp7ndqbh5bqh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14167",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7213285126",
  "pdf_url": "https://arxiv.org/pdf/2609.14167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bwp7ndqbh5bqh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Decomposition of Drinfeld cusp forms of level $t$",
  "title_text": "On Decomposition of Drinfeld cusp forms of level t",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/bwp7ndqbh5bqh",
  "venue": "arXiv",
  "versions": []
}