On the \(U_p\) operator acting on \(p\)-adic overconvergent modular forms when \(X_0(p)\) has genus 1

In this article we will show how to compute \(U_p\) acting on spaces of overconvergent \(p\)-adic modular forms when \(X_0(p)\) 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 characte...

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Bibliographic Details
Published in:arXiv.org 2008-10
Main Author: Kilford, L J P
Format: Article
Language:English
Subjects:
Algorithms
Analytic functions
Eigenvectors
Modular construction
Power series
Online Access:Get full text
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Summary:In this article we will show how to compute \(U_p\) acting on spaces of overconvergent \(p\)-adic modular forms when \(X_0(p)\) 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.
ISSN:2331-8422