  Let K be the totally real cubic field of discriminant 49, let O be its ring
of integers, and let p be the prime over 7. Let Gamma (p)\subset Gamma =
SL_2(O) be the principal congruence subgroup of level p. This paper
investigates the geometry of the Hilbert modular threefold attached to Gamma
(p) and some related varieties. In particular, we discover an octic in P^3 with
84 isolated singular points of type A_2.
