Abstract: Given a cuspidal representation of a symplectic group the theta correspondence method returns an automorphic representation of an orthogonal group. It is possible to decide whether the image is cuspidal by considering a tower of theta correspondences. To determine the first place when the image of a given representation is nonzero is the fundamental problem of the theta correspondence method. We give upper and lower bounds for it in terms of the wave front set of the initial representation. This is a joint work with D. Ginzburg