An interesting problem with automorphic forms is counting the number of level one automorphic representations with a given weight and classifying them by (conjectural) global Arthur parameters. In the works of Chenevier-Taïbi-Renard, this problem is considered for many classical groups with small ranks and a compact G_2-type group. I will explain my recent work on this problem for a compact F_4-type group, particularly emphasizing a specific family of representations related to classical modular forms via “exceptional (weighted) theta series”.
