The Cusp Forms of Weight 3 on T 2 ( 2 , 4 , 8 ) Bert

نویسنده

  • DUCO VAN STRATEN
چکیده

The congruence subgroup ^{2, 4, 8) of the group Fi of 4 x 4 integral symplectic matrices is contained in T2(4) and contains T2(8), with Tiin) the principal congruence subgroup of level n . The Satake compactification of the quotient of the three-dimensional Siegel upper half space by T2(2, 4, 8) is shown to be a complete intersection of ten quadrics in P13 . We determine the space of global holomorphic three forms on this space, which coincides with the space of cusp forms of weight 3 on T2(2, 4, 8) ; it has dimension 2283. Finally, we study the action of the Hecke operators on this space and consider the Andrianov L-functions of some eigenforms.

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تاریخ انتشار 2010