OFFSET
0,3
COMMENTS
A034599 is almost certainly the same sequence. That will follow if R_20 is a 2-modular lattice. - N. J. A. Sloane, Sep 23 2019
Theta series is a weight 10 modular form for Gamma_0(2). - Andy Huchala, May 13 2023
LINKS
Andy Huchala, Table of n, a(n) for n = 0..20000
C. Bachoc, Voisinage au sens de Kneser pour les réseaux quaternioniens, Comment. Math. Helvetici 70 (1995), 350-374.
C. Bachoc and G. Nebe, Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order, Experiment. Math. 6 (1997), 151-162.
G. Nebe and N. J. A. Sloane, Home page for this lattice
EXAMPLE
G.f. = 1 + 3960*q^4 + 168960*q^6 + ...
PROG
(Magma)
prec := 10;
ls := [4, 0, 4, 0, 0, 4, 2, 2, 2, 4, 0, 0, -2, -1, 4, 0, 0, 0, 1, 0, 4, 2, 0, 0, 1, 0, 0, 4, 1, -1, -1, 0, 2, 2, 2, 4, 1, -1, -1, 0, 1, 1, 1, 1, 4, 1, 1, 1, 2, -1, 1, -1, -1, 0, 4, 1, -1, 1, 0, -1, 1, 1, 1, 0, 0, 4, 1, -1, 1, 1, 0, 2, 0, 1, 2, 2, 2, 4, -1, 1, 1, 0, -1, -1, -1, -2, -2, 0, 0, -1, 4, -1, -1, -1, -2, 1, -1, -1, 0, 0, -2, 0, -1, 0, 4, -1, 1, -1, 0, 1, 1, -1, 0, 0, 0, -2, -1, 0, 0, 4, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -2, 2, 2, 2, 4, 1, -1, 1, 1, 0, 0, 0, 0, 1, 1, -1, 1, -2, 0, 0, -1, 4, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, 1, 1, 0, -2, 0, -1, 0, 4, -1, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1, 1, 0, 0, -2, -1, 0, 0, 4, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -2, 2, 2, 2, 4];
S := SymmetricMatrix(ls);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
coeffs := [1, 0, 3960];
Coefficients(&+[coeffs[i]*B[i] :i in [1..3]]); // Andy Huchala, May 13 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Andy Huchala, May 13 2023
STATUS
approved