Normalized supercharacter formula for integrable osp(3|2) modules

Let $L(\Lambda)$ be an integrable nonzero-level module over the affine Lie superalgebra in the surrounding section, with $\Lambda\in\Omega_k$ or $\Lambda\in\Omega'_k$. Define $\overline{W}$ and $c_{\Lambda}$ according to the module's $\alpha_0+\alpha_1$- and $\alpha_2+\alpha_3$-integrability, and let $\Theta^L_{\Lambda,T}$ (or $\Theta^L_{\Lambda,T'}$) be the associated theta expression. Normalized supercharacter formula.

$$\widehat{R}^{-}\operatorname{ch}^{-}_{\Lambda}=\frac{1}{c_{\Lambda}}\sum_{w\in\overline{W}}\varepsilon^{-}(w)w\left(\Theta^L_{\Lambda,T\,\text{(respectively }T')}\right).$$

The displayed formula is presented as a conjectural analogue of the earlier formula; its status is not resolved in the supplied text.