Integral modular data and congruences

We compute all fusion algebras with symmetric rational S-matrix up to dimension 12. Only two of them may be used as S-matrices in a modular datum: the S-matrices of the quantum doubles of ℤ/2ℤ and S ₃. Almost all of them satisfy a certain congruence which has some interesting implications, for example for their degrees. We also give explicitly an infinite sequence of modular data with rational S- and T-matrices which are neither tensor products of smaller modular data nor S-matrices of quantum doubles of finite groups. For some sequences of finite groups (certain subdirect products of S ₃,D ₄,Q ₈,S ₄), we prove the rationality of the S-matrices of their quantum doubles.