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Theta series of the canonical laminated lattice LAMBDA_29.
0

%I #14 Sep 24 2023 10:23:45

%S 1,0,0,0,198506,163840,20662272,45481984,745402040,1904738304,

%T 13582315520,32267304960,152158214640,321893203968,1194291679232,

%U 2263580016640,7176091448362

%N Theta series of the canonical laminated lattice LAMBDA_29.

%C Theta series is an element of the space of modular forms on Gamma_0(16) of weight 29/2 and dimension 30 over the integers.

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 179.

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.2307/2007025">Laminated lattices</a>, 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.

%H J. H. Conway and N. J. A. Sloane, <a href="/A005135/a005135.png">The "shower" showing containments among the laminated lattices up to dimension 48</a> (Fig 3 from the Annals paper, also Fig. 6.1 in the Sphere packing book).

%H G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA29.html">Home page for this lattice</a>

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

%e G.f.: 1 + 198506*q^8 + 163840*q^10 + ...

%o (Magma)

%o L := Lattice("Lambda", 29);

%o T<q> := ThetaSeries(L, 14);

%o C := Coefficients(T);

%o [C[2*i-1] : i in [1..8]];

%Y Cf. A005135, A023942, A008408.

%K nonn,more

%O 0,5

%A _Andy Huchala_, Jun 27 2021

%E a(14)-a(16) from _Robin Visser_, Sep 24 2023