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We give upper bounds to the number of  n -dimensional irreducible complex representations of finite quasisimple groups belonging to different families of groups of Lie type. The bounds have the form  c  n s  , where  c  and  s  are explicit positive constants that both depend on the family in question. From these bounds, we deduce a uniform bound of the form  c  n  to the number of  n -dimensional irreducible representations of all finite quasisimple groups of Lie type. Finally, an application of these results to counting conjugacy classes of maximal subgroups of Lie groups is discussed.

Complex representation growth of finite quasisimple groups of Lie type