Group of automorphisms of a Shimura curve

Let B be the indefinite quaternion algebra over Q of discriminant D. Let O be a maximal order in B. Let XD be the Shimura curve over Q attached to O, whose set of complex points is given by XD(C) = (Ô×\B̂× × P)/B×, where P = C\R. As it is well known, suchXD is equipped with a natural group of involutions called the Atkin-Lehner group W (D), where each involution ωn is indexed by the divisors n | D. Thus the Atkin-Lehner groupW (D) as a subgroup of the group of automorphisms Aut(X0(D,N)) is a 2elementary abelian group isomorphic to (Z/2Z), where r = #{p | D}. The following proposition characterizes Aut(XD) also as a 2-elementary abelian group, in case that the genus is at least 2. Proposition 1.1. [3, Proposition 1.5] Let U ⊆ W (D) be a subgroup and let XD/U denote the quotient curve. If the genus of XD/U is at least 2, then all automorphisms of XD/U are defined over Q and Aut(XD/U) = (Z/2Z) for some s ≥ r − rankF2(U). Remark 1.2. This proposition is also true if we consider Shimura curves with non trivial level.