We use a method of Buzzard to study p-adic famillies of different types of modular forms - classical, over imaginary quadratic fields and totally real fields. In the case of totally real fields of even degree, we get local constancy of dimensions of spaces of fixed slope and varying weight. For imaginary quadratic fields we obtain bounds independent of the weight on the dimensions of such spaces.
Algebra Seminar
Monday, September 11, 2006 - 4:00pm
Aftab Pande
University of Regensburg and Brandeis University