A006910 Theta series of laminated lattice LAMBDA_11^{min}. (Formerly M5452)

1, 0, 432, 1632, 8700, 18048, 51072, 82880, 191926, 251648, 517568, 619104, 1204024, 1322368, 2326528, 2515904, 4396188, 4407552, 7238000, 7303456, 11911352, 11434752, 17948288, 17151936, 27144744, 25129984, 37714368, 35413888, 54674928, 48607872, 72122368

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 11/2, and dimension 22 over the integers. - Andy Huchala, May 05 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, -1, -2, 1, 1, 0, 1, 0, -1, 0, 1, 4]);
L := LatticeWithGram(S);
T<q> := ThetaSeries(L, 45);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1] * B[i] : i in [1..21]] + Coefficients(T)[45]*B[22]); // Andy Huchala, May 05 2023

Crossrefs

Sequence in context: A179666 A203663 A250815 * A015229 A360840 A248460

Adjacent sequences: A006907 A006908 A006909 * A006911 A006912 A006913

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

a(26)-a(30) from Andy Huchala, May 05 2023

Status

approved