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On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
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Cremona, J. E., Dembele, Lassina, Pacetti, Ariel, Schembri, Ciaran and Voight, John (2022) On rational Bianchi newforms and abelian surfaces with quaternionic multiplication. In: Balakrishnan, J. S and Elkies, N. and Hassett, B. and Poonen, B. and Sutherland, A. and Voight, J., (eds.) Arithmetic Geometry, Number Theory, and Computation. Simons Symposia . Springer International Publishing. ISBN 9783030809133
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Official URL: https://www.springer.com/gp/book/9783030809133
Abstract
We study the rational Bianchi newforms (weight 2, trivial character, with rational Hecke eigenvalues) in the LMFDB that are not associated to elliptic curves, but instead to abelian surfaces with quaternionic multiplication. Two of these examples exhibit a rather special kind of behaviour: we show they arise from twisted base change of a classical newform with nebentypus character of order 4 and eight inner twists.
| Item Type: | Book Item | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Series Name: | Simons Symposia | ||||||
| Publisher: | Springer International Publishing | ||||||
| ISBN: | 9783030809133 | ||||||
| Book Title: | Arithmetic Geometry, Number Theory, and Computation | ||||||
| Editor: | Balakrishnan, J. S and Elkies, N. and Hassett, B. and Poonen, B. and Sutherland, A. and Voight, J. | ||||||
| Official Date: | 5 April 2022 | ||||||
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| Number of Pages: | 590 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Copyright Holders: | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG | ||||||
| Date of first compliant deposit: | 5 October 2020 | ||||||
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