OFFSET
0,3
COMMENTS
Theta series is an element of the space of modular forms on Gamma_1(8) with Kronecker character 8, weight 13/2, and dimension 7 over the integers. - Andy Huchala, May 04 2023
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 157.
E. C. Pervin, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Andy Huchala, Table of n, a(n) for n = 0..20000
G. Nebe and N. J. A. Sloane, Home page for this lattice
PROG
(Magma)
prec := 40;
S := SymmetricMatrix([4, 2, 4, 0, -2, 4, 0, -2, 0, 4, 0, 0, -2, 0, 4, -2, -2, 0, 0, 0, 4, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -1, 0, 0, 4, 0, 0, 0, 0, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 1, -2, 0, 1, 0, 0, -1, 1, 0, 0, 4, -1, 0, -1, -1, 1, 0, 1, 0, 1, 1, 0, 0, 4]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 14);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] :i in [1..7]]); // Andy Huchala, May 05 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(11)-a(27) from Andy Huchala, May 05 2023
STATUS
approved