Counting Conjugacy Classes in the Unipotent Radical of Parabolic Subgroups of Gl(N)(Q)

Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GL(n)(q) that is the stabilizer of a flag in F-q(n) of length at most 5, and let U = O-p(P). We prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.