A number of recent advances in Catalan combinatorics have crucially used the values of the trace of Hecke algebras to prove interesting combinatorial results. In this talk, we will explore the standard trace in the case of the affine Hecke algebra. The starting point for our work is a generating function for this trace due to Opdam. The resulting expression for the trace, in terms of Kostant partitions, is closely related to the theory of Tesler matrices and diagonal coinvariants. We will see how the residue theoretic approach of Szenes and Vergne can be used to provide an alternate combinatorial recipe to compute the coefficients of this generating function and look at the combinatorial questions that arise in this analysis.