A006915 Theta series of laminated lattice LAMBDA_13^{min}. (Formerly M5483)

1, 0, 888, 6432, 36392, 110720, 336992, 696512, 1656202, 2779392, 5603904, 8392864, 15385200, 20978048, 35705728, 46190016, 74768920, 92015360, 142090040, 169094496, 255887536, 293745408, 427864224, 485217472, 696300464, 765363200, 1075013440, 1170251136

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 13/2, and dimension 26 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 := 80;
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, -1, -2, 1, 1, 0, 1, 0, -1, 0, 1, 4, 0, -1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 4]);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
T<q> := ThetaSeries(L, 52);
Coefficients(&+[Coefficients(T)[2*i-1] * B[i] : i in [1..25]]+Coefficients(T)[53]*B[26]); // Andy Huchala, May 04 2023

Crossrefs

Sequence in context: A066270 A236981 A203724 * A178270 A183751 A231954

Adjacent sequences: A006912 A006913 A006914 * A006916 A006917 A006918

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(11)-a(27) from Andy Huchala, May 04 2023

Status

approved