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.

Levels 00001-12000 | Levels 12001-24000 | Levels 24001-36000 | Levels 36001-48000 | |||

Levels 48001-60000 | Levels 60001-72000 | Levels 72001-84000 | Levels 84001-96000 |

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