  Over a smooth complex projective curve $C$ of genus $g$ let $\M (n,d)$ be the
moduli space of semistable bundles of rank $n$ and degree $d$ on $C$, and $\SM
(n,L)$, the moduli space of those bundles whose determinant is isomorphic to a
fixed line bundle $L$ over $C$. Let $\theta_F$ and $\theta$ be theta bundles
over these two moduli spaces. We prove a simple formula relating their spaces
of sections: if $h=\gcd (n,d)$ is the greatest common divisor of $n$ and $d$,
and $L\in \Pic ^d(C)$, then $$\dim H^0(\SM (n,L), \theta^k) \cdot k^g=\dim
H^0(\M(n,d),\theta_F^k)\cdot h^g.$$ We also formulate a conjectural duality
between these two types of spaces of sections.
