A345658 - OEIS

%I #17 Sep 24 2023 10:06:37

%S 1,0,0,0,197142,49152,17938944,13565952,500022972,549519360,

%T 7119111168,8746696704,64795688552,80374972416,426695568384,

%U 515432841216,2207141692182,2563069771776,9461992962048

%N Theta series of the canonical laminated lattice LAMBDA_27.

%C Theta series is an element of the space of modular forms on Gamma_0(16) of weight 27/2 and dimension 28 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/LAMBDA27.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 + 197142*q^8 + 49152*q^10 + ...

%o (Magma)

%o L := Lattice("Lambda", 27);

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

%o C := Coefficients(T);

%o [C[2*i-1] : i in [1..7]];

%Y Cf. A005135.

%K nonn,more

%O 0,5

%A _Andy Huchala_, Jun 21 2021

%E a(16)-a(18) from _Robin Visser_, Sep 24 2023