Slopes of modular forms: varying the residual representation

Robert Pollack, Arizona State University

The slope of an eigenform is the p-adic valuation of its U_p-eigenvalue. If we fix a mod p Galois representation rhobar, a standard construction is to consider all modular forms whose residual representation is rhobar. One could, for instance, ask which slopes occur for such eigenforms. In this talk, we will instead vary rhobar and study how the corresponding slopes change. More precisely, we let rhobar range over the EG-stack and study how slopes change from component to component. k