Level one algebraic cusp forms of classical groups of small rank / Gaetan Chenevier and David Renard.

Includes bibliographical references.

Chapter 1. Introduction
Chapter 2. Polynomial invariants of finite subgroups of compact connected Lie groups
Chapter 3. Automorphic representations of classical groups : review of Arthur's results
Chapter 4. Determination of $\Pi _{\rm alg}^\bot ({\rm PGL}_n)$ for $n\leq 5$
Chapter 5. Description of $\Pi _{\rm disc}({\rm SO}_7)$ and $\Pi _{\rm alg}^{\rm s}({\rm PGL}_6)$
Chapter 6. Description of $\Pi _{\rm disc}({\rm SO}_9)$ and $\Pi _{\rm alg}^{\rm s}({\rm PGL}_8)$
Chapter 7. Description of $\Pi _{\rm disc}({\rm SO}_8)$ and $\Pi _{\rm alg}^{\rm o}({\rm PGL}_8)$
Chapter 8. Description of $\Pi _{\rm disc}({\rm G}_2)$
Chapter 9. Application to Siegel modular forms
Appendix A. Adams-Johnson packets
Appendix B. The Langlands group of $\mathbb {Z}$ and Sato-Tate groups
Appendix C. Tables
Appendix D. The $121$ level $1$ automorphic representations of ${\rm SO}_{25}$ with trivial coefficients
Bibliography.

The authors determine the number of level $1$, polarized, algebraic regular, cuspidal automorphic representations of $\mathrm{GL}_n$ over $\mathbb Q$ of any given infinitesimal character, for essentially all $n \leq 8$.