  By a theorem of D. Wigner, an irreducible unitary representation with
non-zero $(\frak{g},K)$-cohomology has trivial infinitesimal character, and
hence up to unitary equivalence, these are finite in number. We have determined
the number of equivalence classes of these representations and the Poincar\'{e}
polynomial of cohomologies of these representations for the Lie group
$SO_0(2,m)$ for any positive integer $m.$ We have also determined, among these,
which are discrete series representations and holomorphic discrete series
representations.
