Conjectural graded dimension formula for the torus state space

Let $\Sigma=S^1\times S^1$ and let $\omega\in H^1(S^1\times S^1;{\mathbb Z}/2{\mathbb Z})$. For a graded vector space, write $\dim_s$ for the sum over $k\in{\mathbb Z}$ of $s^k$ times the dimension of its degree-$k$ subspace. The conjecture. The graded dimension of the associated state space satisfies:

1. If $r\in2{\mathbb Z}+1$, then

$$\dim_s\left(\mathbb{V}(S^1\times S^1)\right)=\frac{3r-1}{2}.$$

2. If $r\in4{\mathbb Z}+2$ and $\omega\neq0$, then

$$\dim_s\left(\mathbb{V}(S^1\times S^1)\right)=\frac{3r-2}{4}.$$

3. If $r\in4{\mathbb Z}+2$ and $\omega=0$, then

$$\dim_s\left(\mathbb{V}(\Sigma)\right)=s^{-1}+\frac{3r+2}{4}+s.$$

These formulas conjecturally extend the computed dimensions from generic to non-generic cohomology classes, including the case where the relevant period of $\omega$ is integral. They give the expected graded dimensions of the skein-module state space for a solid torus bounding the torus.