Computing weight 1 forms -- a p-adic approach

The computation of Hecke-eigenforms of weight at least 2 is readily accomplished through the
theory of modular symbols as these Hecke-eigensystems occur in the cohomology of modular
curves.  However, the same is not true for weight 1 modular forms which makes computing
the dimensions of such spaces difficult let alone the actual system of Hecke-eigenvalues. 
Recently effective methods for computing such spaces have been introduced building on an
algorithm of Kevin Buzzard.  In this talk, we present a different, p-adic approach towards
computing these spaces which yields upper bounds on both their dimension and on the
systems of Hecke-eigenvalues which they can contain.