Author's Comments: Although the principal purpose of this paper was to review how the Selberg trace formula is combined with character formulas to calculate the dimension of various spaces of automorphic forms. it is included as a paper on representation theory because the most influential observation in the paper was the description of a possible realization of the discrete series representations on spaces of \(L^2\)-cohomology.

Editorial comments: This was written in 1973. It first appeared as a preprint distributed by the Institute for Advanced Study, and was later (1988) published by the A.M.S. in Math. Surveys and Monographs 31.

Editorial comments: This has not been published before. It was written around 1977, just after A. Knapp and G. Zuckerman had announced their results on reducible unitary principal series, subsequently explained in a talk at the A.M.S. 1977 summer school in Corvallis (pp. 93-105 of the published proceedings of that conference.)

Author's comments: This paper, or some aspects of this paper, have been called into question in

https://mathoverflow.net/q/144419

A good many years have passed since I wrote the paper, so that I cannot easily verify the validity of the criticisms in the above reference. They appeared several years ago and are very likely valid, but anyone who is currently concerned with these matters can decide for himself. I thank Anthony Pulido and Yvan Saint-Aubin for drawing my attention to the paper and to the criticisms.