Slopes of overconvergent 2-adic modular forms
Number Theory
2007-05-23 v1
Abstract
The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of tame level 1 and weight 0. As a consequence we prove that any finite slope 2-adic overconvergent eigenform of tame level 1 and weight 0 has coefficients in Q_2. These results provide evidence towards conjectures of the first author that predict the slopes of classical p-adic modular forms under a mild ``Gamma_0(N)''-regular hypothesis on p.
Cite
@article{arxiv.math/0311364,
title = {Slopes of overconvergent 2-adic modular forms},
author = {Kevin Buzzard and Frank Calegari},
journal= {arXiv preprint arXiv:math/0311364},
year = {2007}
}
Comments
17 pages