A345657 Theta series of the canonical laminated lattice LAMBDA_26.

1, 0, 0, 0, 196848, 24576, 17356032, 6782976, 448438518, 274735104, 5823343872, 4366565376, 48362165472, 39912726528, 292010062848, 253343072256, 1393763244336, 1241347399680, 5550621292032, 5010361122816

Offset: 0

Author

Andy Huchala, Jun 21 2021

Keywords

• nonn
• more

Comments

Theta series is an element of the space of modular forms on Gamma_1(24) with Kronecker character -3 in modulus 24, weight 13, and dimension 52 over the integers.

Examples

			1 + 196848*q^8 + 24576*q^10 + ...
		

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 178.

Links

• J. H. Conway and N. J. A. Sloane, Laminated lattices, Annals of Math., 116 (1982), pp. 593-620. A revised version appears as Chapter 6 of "Sphere Packings, Lattices and Groups" by J. H. Conway and N. J. A. Sloane, Springer-Verlag, NY, 1988.
• J. H. Conway and N. J. A. Sloane, The "shower" showing containments among the laminated lattices up to dimension 48 (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).
• G. Nebe and N. J. A. Sloane, Home page for this lattice
• Index entries for sequences related to laminated lattices

Crossrefs

Cf. A005135, A023942, A008408.

Programs

Magma

L := Lattice("Lambda", 26);
T := ThetaSeries(L,14);
C := Coefficients(T);
[C[2*i-1] : i in [1..8]];

Extensions

a(17)-a(19) from Robin Visser, Sep 24 2023