Galois representations with quaternion multiplication associated to noncongruence modular forms

A. O.L. Atkin, Wen-ching Winnie Li, Tong Liu, Ling Long

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we study the compatible family of degree-4 Scholl representations ρℓ associated with a space S of weight κ > 2 noncongruence cusp forms satisfying QuaternionMultiplication over a biquadratic extension of ℚ. It is shown that ρℓ is automorphic, that is, its associated L-function has the same Euler factors as the L-function of an automorphic form for GL4 over ℚ. Further, it yields a relation between the Fourier coefficients of noncongruence cusp forms in S and those of certain automorphic forms via the three-term Atkin and Swinnerton-Dyer congruences.

Original languageEnglish (US)
Pages (from-to)6217-6242
Number of pages26
JournalTransactions of the American Mathematical Society
Volume365
Issue number12
DOIs
StatePublished - Oct 2 2013

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Automorphic Forms
Galois Representations
Cusp Form
Modular Forms
L-function
Quaternion
Multiplication
Fourier coefficients
Congruence
Euler
Term
Family

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Galois representations with quaternion multiplication associated to noncongruence modular forms. / Atkin, A. O.L.; Li, Wen-ching Winnie; Liu, Tong; Long, Ling.

In: Transactions of the American Mathematical Society, Vol. 365, No. 12, 02.10.2013, p. 6217-6242.

Research output: Contribution to journalArticle

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