Conjectures of Kudla predict that the intersection multiplicities of special cycles on the integral models of certain Shimura varieties should be related to the Fourier coefficients of automorphic forms. As a particular example, one can take the Shimura variety to be a Hilbert modular surface X. The integral model of X is then an arithmetic threefold which comes equipped with two different types of special cycles. First one has the locus of points on X which admit complex multiplication by the maximal order in a quartic CM field, and this locus is a cycle of codimension two. Second one has the locus of points on X which admit an action by an order in a quaternion algebra. As the quaternionic order varies one obtains the family of Hirzebruch-Zagier divisors. We will show that the intersection multiplicities of the CM cycles with the Hirzebruch- Zagier divisors agree with the Fourier coefficients of a very particular modular form, which arises as the central derivative of a Hilbert modular Eisenstein series. This is joint work with Tonghai Yang.