The spaces of meromorphic Prym differentials on finite tori

In this article we construct all kinds of elementary Prym differentials for arbitrary characters on a variable torus with a finite numbers of punctures and find the dimensions of two important quotient spaces. As a consequence, this yields the dimension of the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters on torus. Also, we construct explicit bases in these quotient spaces.