  The Iwahori-Hecke algebra has a ``natural'' trace $\tau$. This trace is the
evaluation at the identity element in the usual interpretation of the
Iwahori-Hecke algebra as a sub-algebra of the convolution algebra of a p-adic
semi-simple group. The Iwahori-Hecke algebra contains an important commutative
sub-algebra ${\bf C}[\theta_x]$, that was described and studied by Bernstein,
Zelevinski and Lusztig. In this note we compute the generating function for the
value of $\tau$ on the basis $\theta_x$.
