Let $C$ be a smooth projective curve over $\mathbb{C}$ of genus $g$. All the semistable rank 2 vector bundle $E$ with a fixed determinant bundle $L$ form a projective variety $\mathcal{M}_{2, L}$of dimension 3(g-1).

Question: What is the dimension of the locus of normalized ones in $\mathcal{M}_{2, L}$? Can we calculate its class in Chow ring? By "E is normalized", I mean in Hartshorne that $h^0(E)>0$, but $h^0(E\otimes M)=0$ for any negative degree line bundle $M$.

Thanks for reading.