I mean some quadratic field can be embeded into H, my question is how many such field ,is ther finite or infinite many?

And is there any refenreces have explicit computation of the problem?

in the case of Q ,the homomorphisms between groups is characterized by homomorphisms between lie algebra ?

May I ask one more ? is it that beside A-->diag(A,A,A),all others factor through $SP_4$ ,ie.$SL_2$−−>$SP_4$−−>$SP_6$

because I want to see how upper half plane$H_1$ can be holomorphic ibemdding to siegel space $H_3$ as totally geodesic ,see Ichiro Statke's paper"Holomorphic embedding of symmetric domains into a seigel space". And what is the corresponding map of lie groups $SL_2$ to $SP_6$ , if it is arise from map of lie groups? is it just the following type? A-->diag(A,1,1);A-->diag(1,A,1);A-->diag(1,1,A);A-->diag(A,A,1); A-->diag(A,1,A);A-->diag(1,A,A);A-->diag(A,A,A) – TOM 27 secs ago

@Tyler Lawson: I'm a little confused .For Mumford in his paper says"In dimension 1, 2 ,3, all families are characterized by endomorphisms".So any shimura varieties defining families of abelian threefold are PEL type?

@SimponPL: Mumford's example is not arising from $GL_2$asscociated to quaternion algebras,am I right?