Determine the density of the exact Humbert form for discriminant 49

Determine whether the primitive exact Humbert form G_7^49 is nearly dense in its admissible modular-monomial support.

Background

The paper develops a reconstruction method for exact Humbert forms G_n^{n^2} and the defining equations F_n of genus-two split-Jacobian loci. For n=7, the admissible modular support has 526,735 monomials, substantially fewer than the 2,121,445 unrestricted weighted-homogeneous candidates. The observed occupancies of the admissible support increase from 24/26 for n=2 to 23,612/23,650 for n=5, motivating the expectation that the discriminant-49 form may likewise have very few zero coefficients within its admissible support.

The issue matters computationally because near-density would mean that sparsity cannot substantially reduce the size of the n=7 reconstruction problem. The paper does not establish whether the observed occupancy trend persists for G_7^49.