Let G be a unimodular group,
and let λd be the subrepresentation of the left regular representation λ, which is the
sum of the square integrable representations. The purpose of this paper is to study
the representation λd with special emphasis on the closed subspace Ad(G) of the
Fourier algebra A(G) of the group which is generated by the coefficients of λd. In the
last part of the paper we study in detail a particular noncompact group for which
λ = λd.