Abstract
The 2gtheta constants of second kind of genusggenerate a graded ring of dimensiong(g +1)/2. In the caseg ≥3 there must exist algebraic relations. In genusg =3 it is known that there is one defining relation. In this paper we give a relation in the caseg =4. It is of degree 24 and has the remarkable property that it is invariant under the full Siegel modular group and whose Φ-image is not zero. Our relation is obtained as a linear combination of code polynomials of the 9 self-dual doubly-even codes of length 24.
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