The ‘1-loop partition function’ of a rational conformal field theory is a sesquilinear combination of characters, invariant under a natural action of
$\text{S}{{\text{L}}_{2}}(\mathbb{Z})$ , and obeying an integrality condition. Classifying these is a clearly defined mathematical problem, and at least for the affine Kac-Moody algebras tends to have interesting solutions. This paper finds for each affine algebra
$B_{r}^{\left( 1 \right)}$ and
$D_{r}^{(1)}$ all of these at level
$k\le 3$ . Previously, only those at level 1 were classified. An extraordinary number of exceptionals appear at level 2—the
$B_{r}^{(1)},D_{r}^{(1)}$ level 2 classification is easily the most anomalous one known and this uniqueness is the primary motivation for this paper. The only level 3 exceptionals occur for
$B_{2}^{(1)}\cong C_{2}^{(1)}$ and
$D_{7}^{(1)}$ . The
${{B}_{2,3}}$ and
${{D}_{7,3}}$ exceptionals are cousins of the
${{\varepsilon }_{6}}$ -exceptional and
${{\varepsilon }_{8}}$ -exceptional, respectively, in the
$\text{A-D-E}$ classification for
$A_{1}^{(1)}$ , while the level 2 exceptionals are related to the lattice invariants of affine
$u(1)$ .