Let $N\in \text{Mat}(10 \times 10,\mathbb{C})$ be nilpotent. Furthermore let $\text{dim} \ker N =3 $, $\text{dim} \ker N^2=6$ and $\text{dim} \ker N^3=7$. What is the Jordan Normal Form?

The only thing I know is that there have to be three blocks, since $\text{dim} \ker N = 3$.

Thank you very much in advance for your help.