are of the form $\bpm a &b\\b &1\epm = -(a+1)(\alpha_0+\alpha_1) + b\alpha_1 - \alpha_{-1}$ with $a-b^2\geq -1$ so $a\geq -1$. The affine Weyl group of $\cF_0$ is an infinite dihedral group generated by $r_0$ and $r_1$, and it preserves each level. Each root on level 1 is equivalent by the affine Weyl group to one of the form $\bpm a &0\\0 &1\epm = -(a+1)(\alpha_0+\alpha_1) - \alpha_{-1}$, and because level 1, $\cF_1$, is a single irreducible $\cF_0$-module (the basic module), the multiplicity of that root is a value of the classical partition function, $p(a+1)$ [@FL]. Each root on level 2 is equivalent by the affine Weyl group to one of the form $\bpm a &0\\0 &2\epm$ or $\bpm a &1\\1 &2\epm$. The $\cF_0$-module structure of level 2 is much more subtle, being the antisymmetric tensors in $\cF_1\otimes\cF_1$ with one irreducible module removed. If we form a generating function of the level 2 root multiplicities in those two columns, $$\sum_{a=0}^\infty {\rm Mult}\bpm a &1\\1 &2\epm\ q^{2a} + 
{\rm Mult}\bpm a &0\\0 &2\epm\ q^{2a+1}$$ it is remarkable that the first 20 coefficients are again given by the partition function $p(\det(N)+1)$. The exact formula for that generating function $$\left[\sum_{n\geq 0} p(n) q^n\right] \left[\prod_{j\geq 1} 