Explicit Methods for Hilbert Modular Forms of Weight 1
Abstract
In this article we present an algorithm that uses the graded algebra structure of Hilbert modular forms to compute the adelic -expansion of Hilbert modular forms of weight one as the quotient of Hilbert modular forms of higher weight. The main improvement to existing methods is that our algorithm can be applied in weight , which fills a gap left by standard computational methods. Additionally, the algorithm can be used to compute Hilbert modular forms over finite fields in all characteristic simultaneously. We use this algorithm to compute a first candidate of a Hilbert modular form of parallel weight that is non-liftable and specify the exact conditions under which our candidate -expansion corresponds to a non-liftable Hilbert Modular form.
Cite
@article{arxiv.1710.02287,
title = {Explicit Methods for Hilbert Modular Forms of Weight 1},
author = {Jasper Van Hirtum},
journal= {arXiv preprint arXiv:1710.02287},
year = {2020}
}
Comments
Several and drastic changes made to the article. In particular, we now only deal with parallel weight. Moreover, we no longer claim a proven example but instead specify the conditions under which the example is proven to be correct