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A239917 Theta series of 16-dimensional lattice OBW16, an overlattice of the Barnes-Wall lattice BW16. 1
1, 0, 0, 512, 4320, 18432, 61440, 193536, 522720, 1126400, 2211840, 4584960, 8960640, 14764032, 23224320, 40221696, 67154400, 96546816, 135168000, 210332160, 319809600, 423976960, 550195200, 801119232, 1147643520, 1436147712, 1771683840, 2462397440, 3371915520 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
The 512 vectors of norm 3 form a spherical 5-design (see Neumaier, 1981). The corresponding configuration of 256 lines in 16-space was studied by Shult and Yanushka, 1980.
This theta series is an element of the space of modular forms on Gamma_0(4) of weight 8 and dimension 5. - Andy Huchala, May 15 2023
LINKS
G. Nebe and N. J. A. Sloane, Home page for this lattice
A. Neumaier, Combinatorial configurations in terms of distances, Report 81-09-Wiskunde, Tech. Univ. Eindhoven, 1981.
A. Neumaier, Lattices of simplex type, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 145--160. MR0699768 (85f:05040). See Example 3.
Ernest Shult, Arthur Yanushka, Arthur, Near n-gons and line systems, Geom. Dedicata 9 (1980), no. 1, 1--72. MR0566437 (82b:51018).
EXAMPLE
The theta series is 1 + 512*q^3 + 4320*q^4 + 18432*q^5 + 61440*q^6 + 193536*q^7 + 522720*q^8 + 1126400*q^9 + 2211840*q^10 + 4584960*q^11 + 8960640*q^12 + 14764032*q^13 + 23224320*q^14 + 40221696*q^15 + 67154400*q^16 + O(q^17).
PROG
(Magma)
L:=LatticeWithGram(16, [3,
-1, 3,
-1, -1, 3,
1, -1, 1, 3,
0, 1, 0, -1, 3,
-1, 0, 0, -1, -1, 3,
1, 0, 0, 1, -1, -1, 3,
-1, 0, 1, 0, 1, -1, -1, 3,
1, 0, -1, 0, -1, 1, 1, -1, 3,
-1, 0, 1, 0, -1, 0, 0, 1, -1, 3,
0, 1, 0, 1, 0, 0, 1, -1, 0, 0, 3,
1, -1, 1, 1, -1, 0, 1, -1, 0, 0, 0, 3,
-1, 0, 1, 1, 0, -1, 0, 1, -1, 1, 0, 0, 3,
0, 0, 1, 0, 1, 0, -1, 1, -1, 0, 0, 0, -1, 3,
1, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, -1, 1, 3,
1, -1, -1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 3]);
T<q>:=ThetaSeries(L, 16);
T;
CROSSREFS
Sequence in context: A186798 A017067 A186845 * A114287 A061209 A017259
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 13 2014
EXTENSIONS
More terms from Andy Huchala, May 15 2023
STATUS
approved

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Last modified April 22 20:16 EDT 2024. Contains 371906 sequences. (Running on oeis4.)