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 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Galois representations with quaternion multiplication associated to noncongruence modular forms'. Together they form a unique fingerprint.

  • Cite this