Asymptotic of $\sum_{k=0}^{\lfloor n^{1-a} \rfloor} \frac{(n^{2(1-a)})^k}{(k!)^2}$

Question

Let $a \in (0,1)$, what is the asymptotic behaviour of $\displaystyle{S_n := \sum_{k=0}^{\lfloor n^{1-a} \rfloor} \frac{(n^{2(1-a)})^k}{(k!)^2}}$ ?

More precisely, is it possible to have an asymptotic equivalence, or at least an upper-bound/lower-bound ?