A006909 Theta series of laminated lattice LAMBDA_10. (Formerly M5439)

1, 0, 336, 768, 4950, 6912, 22944, 27648, 75792, 72192, 181728, 158976, 393030, 317952, 682656, 557568, 1249686, 912384, 1881840, 1458432, 2979072, 2155776, 4254048, 3055104, 6251808, 4354560

Offset

0,3

Comments

This is the q-expansion corresponding to the vector [1, 0, 336, 768, 4950, 6912, 22944, 27648, 75792, 72192, 181728, 158976] in the space of modular forms on Gamma_1(12) with character Kronecker character -3 in modulus 12, weight 5, and dimension 11 over Integer Ring in the basis ordered by degree of leading term (as in Magma).

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

Example

G.f.: 1 + 336*q^4 + 768*q^6 + 4950*q^8 + ...

Prog

(Sage)
e = DirichletGroup(12).1
M = ModularForms(e, 5, QQ)
bases = [_.q_expansion(20) for _ in M.integral_basis()]
list(sum(x*y for (x, y) in zip(bases, [1, 0, 336, 768, 4950, 6912, 22944, 27648, 75792, 72192, 181728, 158976]))) # Andy Huchala, Jun 05 2021

Crossrefs

Sequence in context: A247530 A064259 A181256 * A067708 A377134 A059467

Adjacent sequences: A006906 A006907 A006908 * A006910 A006911 A006912

Keyword

nonn

Author

N. J. A. Sloane

Status

approved