cp's OEIS Frontend

A045867 Theta series of quadratic form with Gram matrix [ 4, 1, 2, 1; 1, 4, 1, 0; 2, 1, 6, -2; 1, 0, -2, 20 ].

%I A045867 #23 Sep 08 2022 08:44:56
%S A045867 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 A045867 24,34,40,12,60,24,34,18,36,30,50,2,40,30,60,34,70,30,64,64,52,42,72,
%U A045867 42,60,50,72,34,62,38,80,54,72,36,100,52,56,76,90,52,126,36,80,72,100
%N A045867 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 A045867 This is the 4-dimensional Elkies_C lattice.
%H A045867 John Cannon, <a href="/A045867/b045867.txt">Table of n, a(n) for n = 0..5000</a>
%H A045867 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 A045867 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 A045867 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 A045867 (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 A045867 (Magma) A := Basis( ModularForms( Gamma0(37), 2), 71); A[1] + 4*A[3]; /* _Michael Somos_, Mar 30 2015 */
%Y A045867 Dual lattice to A045866.
%K A045867 nonn
%O A045867 0,3
%A A045867 _N. J. A. Sloane_
%E A045867 More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000