  We present a semiclassical expansion of the smooth part of the density of
states in potentials with some form of symmetry. The density of states of each
irreducible representation is separately evaluated using the Wigner transforms
of the projection operators. For discrete symmetries the expansion yields a
formally exact but asymptotic series in $\hbar$, while for the rotational
$SO(n)$ symmetries the expansion requires averaging over angular momentum as
well as energy. A numerical example is given in two dimensions, in which we
calculate the leading terms of the Weyl expansion as well as the leading
periodic orbit contributions to the symmetry reduced level density.
