Motivated by the S-duality conjecture, A. Gholampour and A. Sheshmani study the Donaldson–Thomas invariants of the 2-dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular curve. In the case where X is a K3 fibration, they express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K3 fiber and the Noether–Lefschetz numbers of the fibration. A. Gholampour and A. Sheshmani prove that a certain generating function of these invariants is a vector modular form of weight −3/2 as predicted in S-duality.