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Theta series of laminated lattice LAMBDA_25 with minimal norm 4.
1

%I #37 May 07 2023 05:29:46

%S 1,0,0,0,196656,8192,16967424,2260992,414835410,91570176,5027174400,

%T 1453260800,39049024416,13212672000,221932184576,82994429952

%N Theta series of laminated lattice LAMBDA_25 with minimal norm 4.

%C Theta series is an element of space of modular forms on Gamma_1(128) with Kronecker character 8 in modulus 128, weight 25/2, and dimension 192 over the integers. - _Andy Huchala_, May 04 2023

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 177.

%H Andy Huchala, <a href="/A024211/a024211_1.txt">Magma program</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA25.html">Home page for this lattice</a>

%H <a href="/index/La#laminated">Index entries for sequences related to laminated lattices</a>

%e Derivation from Leech lattice sequences A004034 and A008408:

%e .........1 = .........................1

%e .........0 = .........................0

%e .........0 = ............0.+..........0.+.........0

%e .........0 = ............0.+..........0.+.........0

%e ....196656 = ...........48.+.....196560.+........48

%e ......8192 = .........4096.+..........0.+......4096

%e ..16967424 = ........97152.+...16773120.+.....97152

%e ...2260992 = ......1130496.+..........0.+...1130496

%e .414835410 = 1.+...8400704.+..398034000.+...8400704.+.1

%e ..91570176 = 0.+..45785088.+..........0.+..45785088.+.0

%e 5027174400 = 0.+.198896640.+.4629381120.+.198896640.+.0

%e G.f. = 1 + 19665x*q^32 + 8192*q^40 + 16967424*q^48 + ...

%K nonn,more

%O 0,5

%A _N. J. A. Sloane_

%E Corrected and extended by Edward Pervin, Jun 10 2002

%E a(11)-a(15) from _Andy Huchala_, May 04 2023