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Unramified Hilbert modular forms, with examples relating to elliptic curves

Socrates, Jude and Whitehouse, David (2005) Unramified Hilbert modular forms, with examples relating to elliptic curves. Pacific Journal of Mathematics, 219 (2). pp. 333-364. ISSN 0030-8730.

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We give a method to explicitly determine the space of unramified Hilbert cusp forms of weight two, together with the action of Hecke, over a totally real number field of even degree and narrow class number one. In particular, one can determine the eigenforms in this space and compute their Hecke eigenvalues to any reasonable degree. As an application we compute this space of cusp forms for Q(root 509), and determine each eigenform in this space which has rational Hecke eigenvalues. We find that not all of these forms arise via base change from classical forms. To each such eigenform f we attach an elliptic curve with good reduction everywhere whose L-function agrees with that of f at every place.

Item Type:Article
Additional Information:© Copyright 2005, Pacific Journal of Mathematics. Received January 6, 2004. Revised July 1, 2004. Both authors thank their advisor, Dinakar Ramakrishnan, for his support and guidance through this work. They also thank Don Blasius for comments on an earlier version of this paper, Barry Mazur for his encouragement and the referee for a thorough report that led to several improvements in the exposition.
Subject Keywords:Hilbert modular forms, elliptic curves, everywhere good reduction, theta-series, algebras
Record Number:CaltechAUTHORS:SOCpjm05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:807
Deposited By: Tony Diaz
Deposited On:06 Oct 2005
Last Modified:26 Dec 2012 08:41

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