In this paper we study a certain class of irreducible representations of the Lie algebra K of all polynomial vector fields preserving a contact structure. The Lie algebra K admits a triangular decompositionand we can associate to any character τ of Koa Verma module V(τ). Using a method of caracteristic variety, we prove that if τ is not trivial then V(τ) is simple. Then we deduce a formula for the dimension of homogenous components of V(τ)