On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
Number Theory
2020-08-06 v2
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.
Cite
@article{arxiv.1907.12103,
title = {On rational Bianchi newforms and abelian surfaces with quaternionic multiplication},
author = {John Cremona and Lassina Dembélé and Ariel Pacetti and Ciaran Schembri and John Voight},
journal= {arXiv preprint arXiv:1907.12103},
year = {2020}
}
Comments
Revision based on referees comments; 17 pages