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

L. J. P. Kilford

paper

On the $U_{p}$ operator acting on $p$ -adic overconvergent modular forms when $X_{0} (p)$ has genus 1

arXiv:0810.4788

Abstract

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.

10 pages

References in corpus (1)

Spectral expansions of overconvergent modular functions

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

Abstract

References in corpus (1)

On the $U_{p}$ operator acting on $p$ -adic overconvergent modular forms when $X_{0} (p)$ has genus 1