In this paper we explicitly classify all modular invariant partition functions for A (1) r at level 2 and 3. Previously, these were known only for level 1. The level 2 exceptionals exist at r = 9, 15, and 27; the level 3 exceptionals exist at r = 4, 8, and 20. One of these is new, but the others were all anticipated by the “rank-level duality” relating A (1) r level k and A (1) k−1 level r+1. T...