Cremona, J. E., Dembele, Lassina, Pacetti, Ariel, Schembri, Ciaran and Voight, John (2021) 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 (In Press)

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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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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:	15 October 2021
Dates:	Date Event 15 October 2021 Published
Number of Pages:	590
Status:	Peer Reviewed
Publication Status:	In Press
Related URLs:	Publisher Other

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