login
Theta series of 20-dimensional lattice L_20 with group 2.M_22.2.
1

%I #15 Jun 14 2024 22:31:09

%S 1,0,0,0,6160,27104,157080,633600,2152920,6049120,15601432,37243360,

%T 81265800,166554080,325036800,603357216,1082004000,1863350720,

%U 3121660080,5069606080,8058310568,12471782400,19002534320,28292374880,41585775000,59922289504,85450069320

%N Theta series of 20-dimensional lattice L_20 with group 2.M_22.2.

%C This theta series is an element of the space of modular forms on Gamma_0(7) of weight 10 and dimension 7. - _Andy Huchala_, May 15 2023

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. 39.

%H Andy Huchala, <a href="/A033288/b033288.txt">Table of n, a(n) for n = 0..10000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/L20.html">Home page for this lattice</a>

%o (Magma)

%o prec := 30;

%o gram := [8,2,8,-1,0,8,0,-2,0,8,2,-1,-2,4,8,-2,0,-1,-1,-1,8,-2,-1,0,-1,-2,0,8,0,-1,0,-1,-2,-2,-1,8,0,0,-1,-2,-1,0,0,-1,8,1,1,0,2,2,0,0,0,0,8,1,4,2,-2,-1,-2,-2,2,-2,0,8,-4,-2,2,0,0,0,-1,-1,1,0,-1,8,4,0,-1,0,1,-2,2,0,-1,-2,1,-4,8,-4,1,0,-1,0,-1,0,0,-1,-1,2,2,0,8,-2,-2,-4,4,2,0,2,-1,-2,0,-2,0,0,-1,8,4,1,-2,2,2,2,-2,-2,-1,-1,-1,-4,4,-2,1,8,2,-1,-2,-1,0,0,-1,-2,-1,-2,-2,-1,0,-2,2,2,8,-2,0,0,-2,-2,-1,1,0,0,-1,2,1,-1,0,2,-2,2,8,0,0,-1,-2,-1,0,0,2,4,-4,-2,-1,0,-1,-2,0,0,1,8,4,1,-1,-2,1,-2,1,-4,0,-2,1,-1,4,0,0,2,4,2,-1,8];

%o S := SymmetricMatrix(gram);

%o L := LatticeWithGram(S);

%o T := ThetaSeriesModularForm(L);

%o Coefficients(PowerSeries(T,prec)); // _Andy Huchala_, May 15 2023

%K nonn

%O 0,5

%A _N. J. A. Sloane_

%E More terms from _Andy Huchala_, May 15 2023