In this note we will show how to compute Up 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 Up operator and eigenvectors of finite slope for Up, and present some explicit examples. We...

In this brief article we prove local-global compatibility for holomorphic Siegel modular forms with Iwahori level. In previous work we proved a weaker version of this result (up to a quadratic twist) and one of the goals of this article is to remove this quadratic twist by different methods, using p-adic families. We further study the local Galois representation at p for nonregular holomorphic ...

We present an explicit set of matrices giving the action of the Hecke operators T (p), Tj(p ) on Siegel modular forms. Introduction It is well-known that the space of elliptic modular forms of weight k has a basis of simultaneous eigenforms for the Hecke operators, and the Fourier coefficients of an eigenform (and hence the eigenform) are completely determined by its eigenvalues and first Fouri...