  Let X be a complex projective curve which is smooth and irreducible of genus
2. The moduli space M_2 of semistable symplectic vector bundles of rank 4 over
X is a variety of dimension 10. After assembling some results on vector bundles
of rank 2 and odd degree over X, we construct a generically finite cover of M_2
by a family of 5-dimensional projective spaces, and outline some applications.
