  Let $H$ be an ultraspherical hypergroup associated to a locally compact group
$ G $ and let $A(H)$ be the Fourier algebra of $H$. For a left Banach
$A(H)$-submodule $X$ of $VN(H)$, define $Q_X$ to be the norm closure of the
linear span of the set $\{uf: u\in A(H), f\in X\}$ in $B_{A(H)}(A(H), X^*)^*$.
We will show that $B_{A(H)}(A(H), X^*)$ is a dual Banach space with predual
$Q_X$, we characterize $Q_X$ in terms of elements in $A(H)$ and $ X$.
Applications obtained on the multiplier algebra $ M(A(H))$ of the Fourier
algebra $ A(H)$. In particular, we prove that $ G $ is amenable if and only if
$ M(A(H))= B_{\lambda}(H)$, where $B_{\lambda}(H) $ is the reduced
Fourier-Stieltjes algebra of $ H $. Finally, we investigate some
characterizations for an ultraspherical hypergroup to be discrete.
