A103936 Theta series of Barnes-Wall lattice in 64 dimensions.

1, 0, 0, 0, 9694080, 0, 89754255360, 10164979630080, 639876527832960, 24647440237854720, 646038471835975680, 12399979575839293440, 184026095698230213120, 2200347840694273966080, 21889196776341251850240, 185813171532073386639360, 1373979253438910041038720

Offset

0,5

References

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

Links

Andy Huchala, Table of n, a(n) for n = 0..20000

Index entries for sequences related to Barnes-Wall lattices

Example

1 + 9694080*q^8 + 89754255360*q^12 + 10164979630080*q^14 + 639876527832960*q^16 + 24647440237854720*q^18 + 646038471835975680*q^20 + 12399979575839293440*q^22 + 184026095698230213120*q^24 + 2200347840694273966080*q^26 + ...
In terms of H1 = theta_{D4} and H2 = (eta(q) eta(q^2))^8: H1^16 - 384*H1^12*H2 + 38016*H1^8*H2^2 - 743424*H1^4*H2^3 + 9732096*H2^4.

Prog

(Sage)
from sage.modular.etaproducts import qexp_eta; bound = 20;
eta(q) = qexp_eta(ZZ[['q']], bound);
R.<q> = ZZ[];
H1 = ModularForms( Gamma0(2), 2, prec=bound).0;
H1 = R(H1.q_expansion());
H2 = R(q*(eta(q)*eta(q^2))^8);
f = H1^16-384*H1^12*H2+38016*H1^8*H2^2-743424*H1^4*H2^3+9732096*H2^4;
list(f)[:bound] # Andy Huchala, May 01 2021

Crossrefs

Sequence in context: A250518 A268252 A251504 * A147713 A348072 A123322

Adjacent sequences: A103933 A103934 A103935 * A103937 A103938 A103939

Keyword

nonn

Author

Eric Rains and N. J. A. Sloane, Sep 27 2005

Status

approved