cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A345661 Theta series of the canonical laminated lattice LAMBDA_30.

This page as a plain text file.
%I A345661 #7 Sep 24 2023 09:38:26
%S A345661 1,0,0,0,200046,294912,23779584,82378752,1032132696,3570794496,
%T A345661 21539288064,64122912768,266965225878,683889819648,2273486860032,
%U A345661 5134106886144
%N A345661 Theta series of the canonical laminated lattice LAMBDA_30.
%C A345661 Theta series is an element of the space of modular forms on Gamma_1(24) with Kronecker character -3 in modulus 24, weight 15, and dimension 60 over the integers.
%D A345661 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 179.
%H A345661 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 A345661 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 A345661 G. Nebe and N. J. A. Sloane, <a href="https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA30.html">Home page for this lattice</a>
%H A345661 <a href="/index/La#laminated">Index entries for sequences related to laminated lattices</a>
%e A345661 1 + 200046*q^8 + 294912*q^10 + ...
%o A345661 (Magma)
%o A345661 L := Lattice("Lambda", 30);
%o A345661 T<q> := ThetaSeries(L,14);
%o A345661 C := Coefficients(T);
%o A345661 [C[2*i-1] : i in [1..8]];
%Y A345661 Cf. A005135, A023942, A008408.
%K A345661 nonn,more
%O A345661 0,5
%A A345661 _Andy Huchala_, Jun 29 2021
%E A345661 a(11)-a(15) from _Robin Visser_, Sep 24 2023