Computing Hilbert modular forms over fields with nontrivial class group

Authors:
Lassina Dembélé;Steve Donnelly
Affiliations:
Institut für Experimentelle Mathematik, Essen, Germany;School of Mathematics and Statistics, University of Sydney, NSW, Sydney, Australia
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

Citing 2
Cited 1

The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Quadratic forms and quaternion algebras: algorithms and arithmetic

Quadratic forms and quaternion algebras: algorithms and arithmetic

Algorithmic Enumeration of Ideal Classes for Quaternion Orders

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We exhibit an algorithm for the computation of Hilbert modularforms over an arbitrary totally real number field of even degree,extending results of the first author. We present some new instancesof the conjectural Eichler-Shimura construction for totally real numberfields over the fields Q(√10) and Q(√85) and their Hilbert class fields,and in particular some new examples of modular abelian varieties witheverywhere good reduction over those fields.