A045867 - OEIS

%I #23 Sep 08 2022 08:44:56

%S 1,0,4,6,2,6,2,6,10,2,8,14,24,10,14,10,26,14,38,14,32,18,14,16,40,20,

%T 24,34,40,12,60,24,34,18,36,30,50,2,40,30,60,34,70,30,64,64,52,42,72,

%U 42,60,50,72,34,62,38,80,54,72,36,100,52,56,76,90,52,126,36,80,72,100

%N Theta series of quadratic form with Gram matrix [ 4, 1, 2, 1; 1, 4, 1, 0; 2, 1, 6, -2; 1, 0, -2, 20 ].

%C This is the 4-dimensional Elkies_C lattice.

%H John Cannon, <a href="/A045867/b045867.txt">Table of n, a(n) for n = 0..5000</a>

%H N. D. Elkies, <a href="http://www.math.harvard.edu/~elkies/modular.pdf">Elliptic and modular curves over finite fields and related computational issues</a>, in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 57.

%e G.f. = 1 + 4*x^2 + 6*x^3 + 2*x^4 + 6*x^5 + 2*x^6 + 6*x^7 + 10*x^8 + 2*x^9 + ...

%e G.f. = 1 + 4*q^4 + 6*q^6 + 2*q^8 + 6*q^10 + 2*q^12 + 6*q^14 + 10*q^16 + ...

%o (PARI) {a(n) = my(G); if( n<0, 0, G = [ 4, 1, 2, 1; 1, 4, 1, 0; 2, 1, 6, -2; 1, 0, -2, 20]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* _Michael Somos_, Apr 02 2006 */

%o (Magma) A := Basis( ModularForms( Gamma0(37), 2), 71); A[1] + 4*A[3]; /* _Michael Somos_, Mar 30 2015 */

%Y Dual lattice to A045866.

%K nonn

%O 0,3

%A _N. J. A. Sloane_

%E More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000