on Q(ζ) and can be identified with "U"3(f) formula_40 "GL"3("S") where "S" = Z["α",½]. Since "S"/("α") = F7, there is a homomorphism of the group Γ1 into "GL"3(F7). This action leaves invariant a 2-dimensional subspace in F73 and hence gives rise to a homomorphism "Ψ" of Γ1 into "SL"2(F7), a group of order 16·3·7. On the other hand, the stabiliser of a vertex is a subgroup of order 21 and "Ψ" is injective on this subgroup. Thus if the congruence subgroup Γ0 is defined as the inverse image under "Ψ" of the 2-Sylow subgroup of "SL"2(F7), the action of