  We study symplectic manifolds $(M^{2l},\omega)$ equipped with a symplectic
torsion-free affine (also called Fedosov) connection $\nabla$ and admitting a
metaplectic structure. Let $\mathcal{S}$ be the so called symplectic spinor
bundle and let $R^S$ be the curvature tensor field of the symplectic spinor
covariant derivative $\nabla^S$ associated to the Fedosov connection $\nabla.$
It is known that the space of symplectic spinor valued exterior differential
2-forms, $\Gamma(M,\bigwedge^2T^*M\otimes {\mathcal{S}}),$ decomposes into
three invariant spaces with respect to the structure group, which is the
metaplectic group $Mp(2l,\mathbb{R})$ in this case. For a symplectic spinor
field $\phi \in \Gamma(M,\mathcal{S}),$ we compute explicitly the projections
of $R^S\phi \in \Gamma(M,\bigwedge^2T^*M \otimes \mathcal{S})$ onto the three
mentioned invariant spaces in terms of the symplectic Ricci and symplectic Weyl
curvature tensor fields of the connection $\nabla.$ Using this decomposition,
we derive a complex of first order differential operators provided the Weyl
tensor of the Fedosov connection is trivial.
