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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 (2021) On rational Bianchi newforms and abelian surfaces with quaternionic multiplication. In: Arithmetic Geometry, Number Theory, and Computation. Simons Symposia . Springer.
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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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science > Mathematics | ||||
Series Name: | Simons Symposia | ||||
Publisher: | Springer | ||||
Book Title: | Arithmetic Geometry, Number Theory, and Computation | ||||
Official Date: | 2021 | ||||
Dates: |
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Date of first compliant deposit: | 5 October 2020 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Forthcoming | ||||
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