A special cubic fourfold is a smooth hypersurface of degree 3 and dimension 4 that contains a surface not homologous to a complete intersection. Special cubic fourfolds give rise to a countable family of Noether?Lefschetz divisors Cd in the moduli space C of smooth cubic fourfolds. These divisors are irreducible 19-dimensional varieties birational to certain orthogonal modular varieties. We use the ?low-weight cusp form trick? of Gritsenko, Hulek, and Sankaran to obtain information about the Kodaira dimension of Cd . For example, if d = 6n + 2, then we show that Cd is of general type for n > 18, n {20, 21, 25}; it has nonnegative Kodaira dimension if n > 13 and n ≠ 15. In combination with prior work of Hassett, Lai, and Nuer, our investigation leaves only twenty values of d for which no information on the Kodaira dimension of Cd is known. We discuss some questions pertaining to the arithmetic of K3 surfaces raised by our results.