The holomorphic quadratic differential has 4g-4 zeros

Question

Consider surface $\Sigma$ in manifold $M$ and consider the local conformal coordinates $z=x+iy$. The second fundamental form has components $h_{11},h_{12},h_{22}$. The quadratic differential form is $$(h_{11}-h_{22}-2ih_{12})dz^2:=qdz^2$$ Then $q$ is holomophic function if the surface has constant mean curvature. Many notes state that the number of zeros of $q$ is $4g-4$ counted with multiplicity where $g$ is the number of genus of the surface. But I don't really understand why it is $4g-4$? Is it from Riemann–Roch theorem? Could anyone explain it in some details? Thank you.