I am trying to compute a basis for $\Omega(W)$ for a translation surface $W$ of genus $3$. How does this work?
Explicitly I am considering the quaternion origami, which may be found in Herrlich's Paper "Introduction to Origamis in Teichmüller Space", section 5.
I know that $\Omega(W)$ is 3-dimensional, but I don't know, how to find differentials on $W$.