Action of Hecke operators on cohomology of modular curves of level two

Abstract

We calculate the action of the p-th Hecke operator and the inertia group on the l-adic cohomology of modular curve of level Γ0(p2) under the assumption p ≥ 13, using only a local geometrical method. We also calculate the action of the p-th Hecke operator and the inertia group on the l-adic cohomology of the Lubin-Tate space of the same level over the maximal unramified extension of \({\mathbb{Q}_p}\).