Antwerp IV: Table 5: Dimensions of Rational Eigenspaces of the Hecke Algebra

Table of Contents

This is a table of the dimensions of the rational eigenspaces of the Hecke algebra T, acting on the differntial forms on H/Gamma0(N), for N <= 300.

The first two columns of the table contain the level N, and its prime factors p1, ..., pr.

The thrid column lists the splitting of the space of all differential forms, old and new, gien by the involutions Wi = W(pi) (i = 1,...,r). The dimensions of the eigenspaces corresponding to the r-tuple of eigenvalues (eps1,...,epsr) of W1,...,Wr are listed in the order 

  eps1 = +1, eps1 = -1 if r = 1;

  (eps1, eps2) = (+1, +1), (+1, -1), (-1,+1), (-1,-1) if r=2;

  (eps1, eps2, eps3) = +++, ++-, +-+, +--, -++, -+-, --+, ---, if r=3;
in case r=4 (N=210) the first row in eps4=+1, the second is eps4=-1. The fourth column contains the dimensions of the rational eigenspaces of the Hecke algebra acting on the subspace consisting of the newforms only. The W-eigenspaces are in the same order as in column 3, and are separated by commas; for each W-eigenspace we list the partition which describes its splitting into rational eigenspaces of T.

David Kohel has created an extension of the Atkin-Lehner splitting data below for all levels N<= 96000.

The dimensions of the rational eigenspaces for at least levels N < 2500 can be deduced from this table of Hecke eigenvalues. Table 5: Dimensions of Rational Eigenspaces of the Hecke Algebra

Table 5: Dimensions of Rational Eigenspaces of the Hecke Algebra


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