We prove that there are exactly 149 genus two curves C defined
over Q such that there exists a nonconstant morphism p : X1(N) ¿ C defined
over Q and the jacobian of C is Q-isogenous to the abelian variety Af attached
by Shimura to a newform f ¿ S2(G1(N)). We determine the corresponding
newforms and present equations for all these curves.