What integer value can be the conductor of a $g$-dimensional abelian variety over $\mathbb Q$?

Fix a positive integer $ g$ . What positive integer $ n$ can be the conductor of a $ g$ -dimensional abelian variety over $ \mathbb Q$ ?

For example, as there is no abelian varieties over $ \mathbb Z$ , $ N$ can not be $ 1$ . And for elliptic curves, $ N$ must be no less than $ 11$ .