Title: Counting non-tempered automorphic forms using endoscopy

Abstract: How many automorphic representations of level n have a specified local factor at the infinite places? When this local factor is a discrete series representation, this question is asymptotically well-undersertood as n grows. Non-tempered local factors, on the other hand, violate the Ramanujan conjecture and should be very rare. We use the endoscopic classification for representations to quantify this rarity in the case of cohomological representations of unitary groups, and discuss some applications to the growth of cohomology of Shimura varieties.