  A representation field for a non-maximal order H in a central simple algebra
A is a subfield of the spinor class field of maximal orders which determines
the set of spinor genera of maximal orders representing H. In our previous work
we have proved the existence of the representation field for several important
families of suborders, like commutative orders, while we have also found
examples where the representation field fails to exist. In this article, we
prove that the representation field is defined for any order H of rank 7 or
lower. The same technique yields the existence of representation fields for any
order in an algebra whose semi-simple reduction is commutative. We also
construct a rank-8 order whose representation field is not defined.
