  A conjecture attributed to Robert Coleman states there should only be
finitely many isomorphism classes for endomorphism algebras of abelian
varieties of fixed dimension over a fixed number field.
  In this paper, we establish new cases of this conjecture, given conditions on
the 2-torsion field. In fact, for the abelian varieties considered, we provide
an explicit list of possible endomorphism algebras. This list is then refined
by studying the minimal extension of the ground field over which all
endomorphisms are defined. In particular, we find conditions which guarantee
this extension is contained in the 2-torsion field.
