A discrete extension of 1,p(2) in SP(4,R) and the modular form of the Barth-Nieto quintic
Abstract
We construct a maximal discrete extension of the paramodular group with a full level-2 structure. The corresponding Siegel variety parametrizes (birationally) the space of Kummer surfaces associated to (1,p)-polarized abelian surfaces with a level-2 structure. In the case p=3 this is related to the Barth-Nieto quintic and in this case we also determine the space of cusp forms of weight 3.
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