{
  "abstract": "We investigate automorphic forms for congruence subgroups of $\\mathrm{SL}(3, \\mathbb{Z})$ that are Iwahori at $p$. In particular, we study the cuspidal cohomology of Iwahori congruence subgroups $\\mathcal{I}(3, p)$, which are comprised of matrices in $\\mathrm{SL}(3, \\mathbb{Z})$ that are upper triangular modulo $p$. In order to work with $\\mathcal{I}(3, p)$, we generalize key results from Ash, Grayson, and Green [J.\\ Number Theory 19 (1984), pp.\\ 412-436]. For levels $\\mathcal{I}(3, p)$ with $p \\leq 227$, we found three levels with nonzero cuspidal classes and were able to compute the action of Hecke operators at two of these levels. These are the first examples of non-essentially-self-dual automorphic representations of trivial cohomological weight that are Steinberg at $p$ appearing at Iwahori level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01776",
  "author_total": 1,
  "authors": [
    {
      "name": "Zachary Porat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xfbjr3ejym0v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01776",
  "fulltext_url": null,
  "id": "9xfbjr3ejym0v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01776",
  "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": "W7207841188",
  "pdf_url": "https://arxiv.org/pdf/2609.01776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xfbjr3ejym0v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01776"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the cuspidal cohomology of Iwahori congruence subgroups of $\\mathrm{SL}(3, \\mathbb{Z})$",
  "title_text": "On the cuspidal cohomology of Iwahori congruence subgroups of SL(3, ℤ)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/9xfbjr3ejym0v",
  "venue": "arXiv",
  "versions": []
}