{
  "abstract": "Let $p$ be an odd prime. Let $F$ be a totally imaginary CM field and $F^+$ be the maximal totally real subfield such that $F/F^+$ is unramified at all finite places, and every place $v | p$ of $F^+$ is split in $F$. We allow arbitrary ramification of $p$ in $F^+$. Let $G$ be a rank two definite unitary group over $F^+$ as defined in [2]. Fix a place $\\mathfrak{p} | p$ in $F$. In this article, we determine explicit local Serre weights at $\\mathfrak{p}$ attached to a modular mod $p$ Galois representation $\\barρ_h$ of the absolute Galois group of $F$, associated to an eigenform $h$ of $G$. The eigenform $h$ has arbitrary weights and small slope at $\\mathfrak{p}$. We also show analogous results for certain Hilbert modular eigenforms with arbitrary ramification of $p$ in the totally real field. The eigenforms come from totally definite and indefinite quaternion algebras over totally real fields, split at places above $p$. In proving our results, we identify the non-singular submodules in quotients of certain symmetric power $\\mathbb{F}_q[\\text{M}_2(\\mathbb{F}_q)]$-modules by Dickson polynomials and their twisted versions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37261",
  "author_total": 2,
  "authors": [
    {
      "name": "Abhik Ganguli"
    },
    {
      "name": "Suneel Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkprzch9sm1jr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37261",
  "fulltext_url": null,
  "id": "fkprzch9sm1jr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37261",
  "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": "W7224095326",
  "pdf_url": "https://arxiv.org/pdf/2610.37261",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkprzch9sm1jr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37261",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37261"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Explicit Serre weights for modular Galois representations of $U(2)$",
  "title_text": "Explicit Serre weights for modular Galois representations of U(2)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/fkprzch9sm1jr",
  "venue": "arXiv",
  "versions": []
}