Abstract
van Geemen and van Straten [B. van Geemen, D. van Straten, The cuspform of weight 3 on Γ 2 ( 2 , 4 , 8 ) , Math. Comp. 61 (1993) 849–872] showed that the space of Siegel modular cusp forms of degree 2 of weight 3 with respect to the so-called Igusa group Γ 2 ( 2 , 4 , 8 ) is generated by 6-tuple products of Igusa theta constants, and each of them are Hecke eigenforms. They conjectured that some of these products generate Saito–Kurokawa representations, weak endoscopic lifts, or D-critical representations. In this paper, we prove these conjectures. Additionally, we obtain holomorphic Hermitian modular eigenforms of GU ( 2 , 2 ) of weight 4 from these representations.
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