A006916 Theta series of laminated lattice LAMBDA_13^{mid}. (Formerly M5484)

1, 0, 890, 6400, 36600, 110080, 337520, 698880, 1649610, 2780160, 5619792, 8387840, 15347280, 20974080, 35834560, 46174720, 74480280, 92062720, 142597450, 169132800, 254916880, 293647360, 429515280, 485235200, 693838000, 765358080, 1078906000, 1170170880

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

Index entries for sequences related to laminated lattices

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

Sequence in context: A250513 A252577 A202528 * A128871 A110726 A204366

Adjacent sequences: A006913 A006914 A006915 * A006917 A006918 A006919

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(11)-a(27) from Andy Huchala, May 05 2023

Status

approved