The Points of a Certain Fivefold over Finite Fields and the Twelfth Power of the Eta Function

Abstract

AbstractIf p is an odd prime, then denote by Fp the field with p elements. We prove that a certain fivefold is modular in the sense that for every odd p, the number of its points over Fp is predicted explicitly by the pth coefficient of the Fourier expansion of the weight 6 modular form η12(2z)