Basic vector valued Siegel modular forms of genus two

We consider the space of all vector-valued holomorphic modular forms f:H_n→Z of transformation type f(MZ)=vr(M)det(CZ+D)ϱ(CZ+D)f(Z). ϱ:GL(n,C)→GL(Z) is a rational representation on a finite dimensional complex vector space Z. These spaces can be collected in a graded A(Γ)-module We treat in this paper some special cases in genus 2. The first one is essentially due to Wieber. Thus we consider a variant of this case and a new example. In this final case the starting weight is 1/2, the starting multiplier system is the theta multiplier system v_ϑ and for ϱ we take the standard representation. In all these cases we will determine the structure of the spaces.