The Fourier coefficients of theta functions have featured prominently in numerous number theory applications and constructions in the Langlands program. For example, they play an important role in the recent work of Friedberg-Ginzburg generalizing the theta correspondence to higher covering groups. For their construction one wants to know the wave front set of the theta representations, i.e. the largest nilpotent orbit with nonvanishing Fourier coefficient.

To investigate these Fourier coefficients it can be valuable to study the analogous local question. In this talk we consider local theta representations and describe how to compute their stable wave front set. This is joint work with Emile Okada and Runze Wang.