order of trace character distribution of irreducible unitary representations of nilpotent groups.

Question

Let $N$ be a simply connected nilpotent group and let $\pi$ be an irreducible unitary representation of $N$. Then for every Schwartzfunction $f \in S(N)$ the integrated Operator $\pi(f)$ is of trace class and the the functional $f \mapsto tr(\pi(f))$ is a (non-regular) distribution on $N$. I am interested in the order of such a distribution. Im currently reading through the book "Lectures on the Orbit Method" by Kirillov and on page 75 he claims that the order of $f \mapsto tr(\pi(f))$ depends on the geometry of the coadjoint orbit which belongs to $\pi$ (in the sense of the Orbit-method of Kirillov). He also says that finding the explicit form of this dependence is still an open problem. Does anyone know if this problem is solved?