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The theta series of the two unimodular even positive definite lattices ofrank 16 are known to be linearly dependent in degree at most 3 and linearlyindependent in degree 4. In this paper we consider the next case of the 24Niemeier lattices of rank 24. The associated theta series are linearlydependent in degree at most 11 and linearly independent in degree 12. Theresulting Siegel cusp form of degree 12 and weight 12 is a Hecke eigenformwhich seems to have interesting properties.

A Siegel cusp form of degree 12 and weight 12