Hecke eigenforms in the cohomology of congruence subgroups of {${\rm SL}(3,\bold Z)$}
van Geemen, Bert ; van der Kallen, Wilberd ; Top, Jaap ; Verberkmoes, Alain
Experiment. Math., Tome 6 (1997) no. 4, p. 163-174 / Harvested from Project Euclid
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We list here Hecke eigenvalues of several automorphic forms for congruence subgroups of $\SL(3,{}$\funnyZ$)$. To compute such tables, we describe an algorithm that combines techniques developed by Ash, Grayson and Green with the Lenstra--Lenstra--Lovász algorithm. With our implementation of this new algorithm we were able to handle much larger levels than those treated by Ash, Grayson and Green and by Top and van Geemen in previous work. Comparing our tables with results from computations of Galois representations, we find some new numerical evidence for the conjectured relation between modular forms and Galois representations.
Publié le : 1997-05-14
Classification:  11F67,  11F75 
@article{1047650002,
     author = {van Geemen, Bert and van der Kallen, Wilberd and Top, Jaap and Verberkmoes, Alain},
     title = {Hecke eigenforms in the cohomology of congruence subgroups of {${\rm SL}(3,\bold Z)$}},
     journal = {Experiment. Math.},
     volume = {6},
     number = {4},
     year = {1997},
     pages = { 163-174},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047650002}
}

van Geemen, Bert; van der Kallen, Wilberd; Top, Jaap; Verberkmoes, Alain. Hecke eigenforms in the cohomology of congruence subgroups of {${\rm SL}(3,\bold Z)$}. Experiment. Math., Tome 6 (1997) no. 4, pp.  163-174. http://gdmltest.u-ga.fr/item/1047650002/