Matrix coefficients of depth-zero supercuspidal representations of $\mathrm{GL}(2)$

Abstract

We give explicit formulas for matrix coefficients of the depth-zero supercuspidal representations of $GL\left(2\right)$ over a nonarchimedean local field, highlighting the case where the test vector is a unit new vector. We also describe the partition of the set of such representations according to central character, and compute sums of matrix coefficients over all representations in a given class.