One of the basic results in the theory of representations of real reductive groups is the Casselman-Wallach theorem connecting algebraic representations to topological representations. We provide a quantitative version of this theorem. For that we introduce the notion of "Sobolev gap" for a Harish-Chandra module. This is a new invariant whose finiteness is highly non-trivial. We determine the Sobolev gap for representations in the unitary dual of the group $SL(2,R)$ and establish uniform finiteness results (for any real reductive group) for representations of the discrete series and the minimal principal series. We then apply these to study automorphic functionals with respect to general lattices in $SL(2,R)$ and prove an abstract convexity bound for them. In my presentation, I will assume no prior knowledge of the representation theory of real reductive groups or the theory of automorphic forms/representations. This is a joint work with Joseph Bernstein, Pritam Ganguly, Bernhard Krötz, Job Kuit