## 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 $$11$$.