Local constancy of dimensions of Hecke eigenspaces of Automorphic forms

Details Local constancy of dimensions of Hecke eigenspaces of Automorphic forms Local constancy of dimensions of Hecke eigenspaces of Automorphic forms

2006-09-13

arxiv.org/abs/math/0609361v2

Journal of Number Theory 129 (2009), pp. 15-27

Mathematics

Number Theory

Revised version which appeared in Journal of Number Theory

Scientific paper

10.1016/j.jnt.2008.06.005

We use a method of Buzzard to study p-adic families 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.

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