For a non-relativistic free particle gas ($E = p^2/2m$), the density of states $g(E)$ scales with energy as:
(A)
g(E) \propto E^{1/2} \text{ in 3 dimensions}
(B)
g(E) \propto E^0 = \text{constant} \text{ in 2 dimensions}
(C)
g(E) \propto E^{-1/2} \text{ in 1 dimension}
(D)
g(E) \propto E^2 \text{ in all dimensions}