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A045865 Theta series of quadratic form with Gram matrix [ 4, 0, 2, 1; 0, 2, 1, 1; 2, 1, 20, 1; 1, 1, 1, 10 ]. 1

%I

%S 1,2,2,4,2,4,8,4,10,6,12,12,16,4,16,16,26,20,26,16,28,20,24,24,40,14,

%T 28,20,40,12,48,16,42,36,36,32,66,2,40,32,60,16,64,40,48,52,48,36,88,

%U 30,62,56,76,32,80,48,80,56,60,56,112,52,64,72,74,56,96,40,68,72,96,28

%N Theta series of quadratic form with Gram matrix [ 4, 0, 2, 1; 0, 2, 1, 1; 2, 1, 20, 1; 1, 1, 1, 10 ].

%C This is the 4-dimensional Elkies_A lattice.

%D N. D. Elkies, Elliptic and modular curves..., in AMS/IP Studies in Advanced Math., 7 (1998), 21-76, esp. p. 57.

%H John Cannon, <a href="/A045865/b045865.txt">Table of n, a(n) for n = 0..5000</a>

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

%e G.f. = 1 + 2*q^2 + 2*q^4 + 4*q^6 + 2*q^8 + 4*q^10 + 8*q^12 + 4*q^14 + 10*q^16 + 6*q^18 + ...

%o (PARI) {a(n) = my(G); if( n<0, 0, G = [ 4, 0, 2, 1; 0, 2, 1, 1; 2, 1, 20, 1; 1, 1, 1, 10 ]; polcoeff( 1 + 2 * x * Ser( qfrep( G, n, 1)), n))}; /* _Michael Somos_, Mar 30 2015 */

%o (MAGMA) A := Basis( ModularForms( Gamma0(37), 2), 72); A[1] + 2*A[2] + 2*A[3]; /* _Michael Somos_, Mar 30 2015 */

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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

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Last modified May 22 04:38 EDT 2022. Contains 353933 sequences. (Running on oeis4.)