A006912 Theta series of laminated lattice LAMBDA_12^{min}. (Formerly M5465)

1, 0, 624, 3456, 17544, 47616, 130752, 252672, 560904, 887808, 1692576, 2412672, 4280736, 5564928, 9068928, 11460864, 17948424, 21310464, 32009904, 37102464, 54842544, 61519872, 87013440, 96555264, 136860576, 146503680, 200463648, 216131328, 294879552

Offset

0,3

Comments

Theta series is an element of the space of modular forms on Gamma_0(8) of weight 6 and dimension 7 over the integers. - Andy Huchala, May 10 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

Example

G.f. = 1 + 624*q^4 + 3456*q^6 + ...

Prog

(Magma)
prec := 30;
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]);
L := LatticeWithGram(S);
M := ThetaSeriesModularFormSpace(L);
B := Basis(M, prec);
Coefficients(&+[Coefficients(T)[2*i-1]*B[i] : i in [1..7]]); // Andy Huchala, May 10 2023

Crossrefs

Sequence in context: A043368 A158374 A349031 * A318939 A223215 A057012

Adjacent sequences: A006909 A006910 A006911 * A006913 A006914 A006915

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Andy Huchala, May 10 2023

Status

approved