  This article considers the relation between the spanning properties of
lattice orbits of discrete series representations and the associated lattice
co-volume. The focus is on the density theorem, which provides a trichotomy
characterizing the existence of cyclic vectors and separating vectors, and
frames and Riesz sequences. We provide an elementary exposition of the density
theorem, that is based solely on basic tools from harmonic analysis,
representation theory, and frame theory, and put the results into context by
means of examples.
