  We give a recursive algorithm for computing the character of the cohomology
of the moduli space $\Mmb_{0,n}$ of stable $n$-pointed genus zero curves as a
representation of the symmetric group $\Sg_n$ on $n$ letters. Using the
algorithm we can show a formula for the maximum length of this character. Our
main tool is connected to the moduli spaces of weighted stable curves
introduced by Hassett.
