  We study over rings of scalar valued Siegel modular forms. modules of vector
valued modular forms of degree two.
  For the two simplest representations, standard and Sym^2, appears rather
natural consider the cases of the group $\Gamma[4,8] $ and $\Gamma[2,4].$
  In these case we give the complete structure of the modules . The main tools
are Theta functions and their derivatives evaluated at $z=0$
