  Howe and Tan (1993) investigated a degenerate principal series representation
of indefinite orthogonal groups $\mathrm{O}(V)$ and explicitly described its
composition series. They showed that there exists a unique unitarizable
irreducible submodule $\Pi$, which is isomorphic to a cohomological
representation. In this paper we construct orthogonal automorphic forms
belonging to $\Pi$ as theta liftings of holomorphic $\mathrm{Mp}_2(\mathbb{R})$
cusp forms by using the Borcherds' method. We will give a useful observation in
computing their Fourier expansions that enables us to give very precise
descriptions of the liftings specially belonging to $\Pi$. We will also
determine the cuspidal supports of the liftings, then confirm the square
integrability of those automorphic forms on orthogonal groups.
