  Chevyrev and Galbraith recently devised an algorithm which inputs a maximal
order of the quaternion algebra ramified at one prime and infinity and
constructs a supersingular elliptic curve whose endomorphism ring is precisely
this maximal order. They proved that their algorithm is correct whenever it
halts, but did not show that it always terminates. They did however prove that
the algorithm halts under a reasonable assumption which they conjectured to be
true. It is the purpose of this paper to verify their conjecture and in turn
prove that their algorithm always halts.
  More precisely, Chevyrev and Galbraith investigated the theta series
associated with the norm maps from primitive elements of two maximal orders.
They conjectured that if one of these theta series "dominated" the other in the
sense that the $n$th (Fourier) coefficient of one was always larger than or
equal to the $n$th coefficient of the other, then the maximal orders are
actually the same. We prove that this is the case.
