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