On the U_p operator acting on p-adic overconvergent modular forms when X₀(p) has genus 1

2008/10/27 by L. J. P. Kilford, Kilford, L. J. P.
Mathematics · #11F03 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11F03

paper · pdf · doi:10.48550/arxiv.0810.4788

10 pages

arxiv created 2008/10/27 · openalex publication_date 2008/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we will show how to compute U_p acting on spaces of overconvergent p-adic modular forms when X₀(p) has genus 1. We first give a construction of Banach bases for spaces of overconvergent p-adic modular forms, and then give an algorithm to approximate both the characteristic power series of the U_p operator and eigenvectors of finite slope for U_p, and present some explicit examples. We will also relate this to the conjectures of Clay on the slopes of overconvergent modular forms.

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