Abstract: Let G be a reductive p-adic group, K a compact open subgroup of G, and \pi a representation of G.  Bernstein’s uniform admissibility theorem states that the dimension of fixed vectors in \pi under K, denoted \dim \pi^K, is bounded independently of \pi.  On the other hand, if \pi is fixed and K varies in a family of principal congruence subgroups of G, \dim \pi^K grows in a manner governed by the Gelfand-Kirillov dimension of \pi.  In this talk, I will present a theorem for GL_N that combines these results by proving a bound for \dim \pi^K that is essentially as strong as the Gelfand-Kirillov bound but which is uniform in \pi.  This is joint work with Rahul Dalal and Mathilde Gerbelli-Gauthier.