Fourier expansions at cusps
Number Theory
2025-09-12 v2
Abstract
In this article we study the fields generated by the Fourier coefficients of modular forms at arbitrary cusps. We prove that these fields are contained in certain cyclotomic extensions of the field generated by the Fourier coefficients at infinity. We also show that this bound is tight in the case of newforms with trivial Nebentypus. The main tool is a result of Shimura on the interplay between the actions of and on modular forms.
Keywords
Cite
@article{arxiv.1807.00391,
title = {Fourier expansions at cusps},
author = {François Brunault and Michael Neururer},
journal= {arXiv preprint arXiv:1807.00391},
year = {2025}
}
Comments
Final accepted version. The v1 of this preprint included an appendix, which is available at [arXiv:1905.02946]