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%I #15 Sep 24 2023 10:23:28
%S 1,0,0,0,202692,516096,29046528,145195008,1538419918,6537101312,
%T 36946043904,124680077312,511130138792,1419643330560,4752698632192
%N Theta series of the canonical laminated lattice LAMBDA_31.
%C Theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 31/2, and dimension 62 over the integers.
%C As of version 2.26-4, the largest rank of a laminated lattice which is recognized by Magma is 31, but laminated lattices of larger rank exist (see Conway and Sloane reference).
%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/LAMBDA31.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 + 202692*q^8 + 516096*q^10 + ...
%o (Magma)
%o L := Lattice("Lambda", 31);
%o T<q> := ThetaSeries(L,14);
%o C := Coefficients(T);
%o [C[2*i-1] : i in [1..8]];
%Y Cf. A005135, A023942, A008408, A002336.
%K nonn,more
%O 0,5
%A _Andy Huchala_, Jun 29 2021
%E a(11)-a(14) from _Robin Visser_, Sep 24 2023