  Using a 0/1 encoding of Young diagrams and its consequences for rim hook
tableaux, we prove a reduction formula of Littlewood for arbitrary characters
of the symmetric group, evaluated at elements with all cycle lengths divisible
by a given integer. As an application, we find explicitly the coefficients in a
formula of Kostant for certain powers of the Dedekind $\eta$-function, avoiding
most of the original machinery.
