  In two previous papers [AGM1, AGM2] we computed cohomology groups
H^5(\Gamma_0 (N); \C) for a range of levels N, where \Gamma_0 (N) is the
congruence subgroup of SL_4 (\Z) consisting of all matrices with bottom row
congruent to (0,0,0,*) mod N. In this note we update this earlier work by
carrying it out for prime levels up to N = 211. This requires new methods in
sparse matrix reduction, which are the main focus of the paper. Our
computations involve matrices with up to 20 million non-zero entries. We also
make two conjectures concerning the contributions to H^5(\Gamma_0 (N); \C) for
N prime coming from Eisenstein series and Siegel modular forms.
