give the obstructions to symplectic embeddings of $k$ balls in $M_{\mu}^{i}$, for $k\geq 8$. We observe that our method can be used, in principle, to compute the packing numbers of any $k$-fold symplectic blow-up of ${\mathbb{CP}}^2$. We also note that D. McDuff and F. Schlenk used a similar method in [@MS] to fully describe the embedding functions of four dimensional ellipsoids into standard balls.

### The Trivial bundle

For the trivial bundle $M_{\mu}^{0}$, our computations of the generalized Gromov widths ${\mathsf{w}}_{k}(M_{\mu}^{0})$ reveal that the obstructions to the embeddings of $k\geq 8$ balls in $M_{\mu}^{i}$ depend in an essential way on the parity of $k$. Indeed, fixing $k\geq 8$ and viewing ${\mathsf{w}}_{k}={\mathsf{w}}_{k}(\mu)$ as a function of $\mu\geq 1$, we show that there are only finitely many obstructions for $k$ odd, while there are infinitely many obstructions for $k$ even.

\[thm:MainTheoremTrivial\] Let $M^0_{\mu}=(S^{2}\times S^{2},\mu\sigma\oplus\sigma)$ with $\mu\geq 1$.

1.  When $k=2p+1$ is odd, the generalized Gromov width ${\mathsf{w}}_{2p+1}(M_{\mu}^{0})$ is given by $${\mathsf{w}}_{2p+1}(M_{\mu}^{0}) =
    \begin{cases}
    c_{\operatorname{vol}}=\sqrt{\frac{ 2 \mu}{2p+1}} & \text{~if~}\mu\in\left[ 1,~ p+1-\sqrt{2p+1} \right)   \\
    \frac{\mu+p}{2p+1}         & \text{~if~}\mu\in\left[ p+1-\sqrt{2p+1},~ p+1 \right) \\
    1                          & \text{~if~}\mu\in\left[ p+1,~ \infty \right)
    \end{cases}$$

2.  When $k=2p$ is even, there exist a decreasing sequence $\{\delta_n\}$ with limit $\lambda = \frac{p-2 