login
Theta series of laminated lattice LAMBDA_21.
0

%I #26 Sep 24 2023 09:27:00

%S 1,0,27720,1272320,19707450,163430400,927305904,3995658240,

%T 14261752680,43493359616,118805241072,292653344256,671496501200,

%U 1430857236480,2904257385888,5571801102336,10326899016378,18297213419520

%N Theta series of laminated lattice LAMBDA_21.

%C Theta series is an element of the space of modular forms on Gamma_0(16) of weight 21/2 and dimension 22 over the integers. - _Andy Huchala_, May 10 2023

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 174.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA21.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 + 27720*q^4 + 1272320*q^6 + ...

%o (Magma)

%o prec := 5;

%o L := Lattice("Lambda",21);

%o T<q> := ThetaSeries(L,2*prec);

%o [Coefficients(T)[2*i-1] : i in [1..prec]]; // _Andy Huchala_, May 10 2023

%K nonn,more

%O 0,3

%A _N. J. A. Sloane_.

%E a(5)-a(16) from _Andy Huchala_, May 10 2023

%E a(17) from _Robin Visser_, Sep 24 2023