For a level N with r distinct prime factors p_1 < ... < p_r we report the dimensions of the eigensubspaces of S_2(X_0(N),Q) associated to the eigenvalues (e_1,..,e_r) in {+1,-1}^r, under dictionary ordering. The corresponding dimensions of new subspaces follow those of the entire cuspidal spaces. This table partially extends Table 5 of Antwerp IV (giving only the Atkin-Lehner decomposition, not the decomposition dimensions of the subspaces).

The decompositions are determined by a theoretical analysis of the ramification points of the Atkin-Lehner operators (as opposed to a computation and decomposition of cusp forms) by an implementation of the formulae in Magma.

The Magma code for computing dimensions of Atkin-Lehner decomposition is atkin-lehner_genera.m.