A006910 - OEIS

%I M5452 #19 May 08 2023 09:36:43

%S 1,0,432,1632,8700,18048,51072,82880,191926,251648,517568,619104,

%T 1204024,1322368,2326528,2515904,4396188,4407552,7238000,7303456,

%U 11911352,11434752,17948288,17151936,27144744,25129984,37714368,35413888,54674928,48607872,72122368

%N Theta series of laminated lattice LAMBDA_11^{min}.

%C Theta series is an element of the space of modular forms on Gamma_1(32) with Kronecker character 8 in modulus 32, weight 11/2, and dimension 22 over the integers. - _Andy Huchala_, May 05 2023

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 157.

%D E. C. Pervin, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andy Huchala, <a href="/A006910/b006910.txt">Table of n, a(n) for n = 0..20000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA11_MIN.html">Home page for this lattice</a>

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

%o (Magma)

%o prec := 40;

%o S := SymmetricMatrix([4,2,4,0,-2,4,0,-2,0,4,0,0,-2,0,4,-2,-2,0,0,0,4,0,0,0,0,0,-2,4,0,0,0,0,0,0,-2,4,0,0,0,0,1,-1,0,0,4,0,0,0,0,-1,0,0,0,0,4,-1,-2,1,1,0,1,0,-1,0,1,4]);

%o L := LatticeWithGram(S);

%o T<q> := ThetaSeries(L, 45);

%o M := ThetaSeriesModularFormSpace(L);

%o B := Basis(M, prec);

%o Coefficients(&+[Coefficients(T)[2*i-1] * B[i] : i in [1..21]] + Coefficients(T)[45]*B[22]); // _Andy Huchala_, May 05 2023

%K nonn

%O 0,3

%A _N. J. A. Sloane_.

%E a(26)-a(30) from _Andy Huchala_, May 05 2023