On local constancy of dimension of slope subspaces of automorphic forms

We prove a higher rank analogoue of a Conjecture of Gouvea-Mazur on local constancy of dimension of
slope subspaces of automorphic forms for reductive groups having discrete series. The proof is based on
a comparison of Bewersdorff's elementary trace formula for pairs of congruent weights and does not
make use of p-adic Banach space methods or rigid analytic geometry.