I am studying automorphic representations of algebraic groups using both classical and representation theoretical approaches. There exist, so called cohomological automorphic representations, which bring a non trivial contribution to the computation of Lie algebra (g, K)-cohomologies, and naturally to the square integrable cohomology of an arithmetic quotient variety. My main interest is focused on analyzing such automorphic representations explicitly as possible. During the year 2003, I studied a kind of Saito-Kurokawa lifting which produces nontempered cohomological residual automorphic forms on PGSp(2). I was successful in describing the Fourier expansions of those lifts explicitly, using a rather classical formulation. Among the results, for instance, the square integrability of the vector-valued lifts was established, which will provide a basis for us to go further and compute the Petersson norms of such lifts. In low rank, or the holomorphic case, such a norm is known to relate precisely to a special value of a certain automorphic L-function and it provides a foundation for the research done by many people on several geometric and arithmetic aspects of such theta lifts. So it will become one of my future research topics in the coming period.