  We study the arithmetic of division fields of semistable abelian varieties A
over the rationals. The Galois group of the 2-division field of A is analyzed
when the conductor is odd and squarefree. The irreducible semistable mod 2
representations of small conductor are determined under GRH. These results are
used in "Paramodular abelian varieties of odd conductor," arXiv:1004.4699.
