  This paper finds for all orthogonal algebras (i.e. the B and D series) all
modular invariant 1-loop partition functions at levels 1,2,3. Previously, only
those at level 1 were classified. An extraordinary number of exceptionals
appear at level 2 -- indeed this is the primary motivation for this paper --
and we find infinitely many new ones there. The only level 3 exceptionals occur
for $B_2$ and $D_7$, and the latter appear to be new. The $B_{2,3}$ and
$D_{7,3}$ exceptionals are cousins of the "$E_6$" and "$E_8$" exceptionals in
the A-D-E classification for affine $A_1$, while the level 2 exceptionals are
related to the lattice invariants of affine u(1).
