  In this article we compute new theta relations which define the moduli space
of abelian surfaces with real multiplication by square root three. We give the
locus of square root three abelian surfaces in terms of the canonical
coordinates on Mumford's moduli space of abelian surfaces with theta structure.
The method that we use to compute the real multiplication theta relations is of
purely algebraic nature. It differs from Runge's method and recent work by
Gruenewald. We expect that our method generalizes to higher discriminants.
