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We compute the class of arithmetic genus two Teichmueller curves in thePicard group of pseudo-Hilbert modular surfaces, distinguished according totheir torsion order and spin invariant. As an application, we compute thenumber of genus two square-tiled surfaces with these invariants. The maintechnical tool is the computation of divisor classes of Hilbert Jacobi forms onthe universal abelian surface over the pseudo-Hilbert modular surface.

Cutting out arithmetic Teichmueller curves in genus two via Theta functions