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By adapting the work of Kudla and Millson we obtain a lifting of cuspidalcohomology classes for the symmetric space associated to GO(V) for anindefinite rational quadratic space V of even dimension to holomorphic Siegelmodular forms on GSp_n(A). For n=2 we prove Thom's Lemma for hyperbolic3-space, which together with results of Kudla and Millson imply aninterpretation of the Fourier coefficients of the theta lift as periodintegrals of the cohomology class over certain cycles. This allows us to provethe p-integrality of the lift for a particular choice of Schwartz function foralmost all primes p. We further calculate the Hecke eigenvalues (including forsome "bad" places) for this choice in the case of V of signature (3,1).

Arithmetic properties of similitude theta lifts from orthogonal to symplectic groups