Search: id:A029713
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%I A029713
%S A029713 1,0,30,56,66,144,188,288,378,448,528,504,884,1008,1056,1440,1290,1344,
%T A029713 1834,1848,2064,2880,2652,3168,3332,2688,3696,3696,4128,5040,5280,5760,
%U A029713 5610,5824,6012,5376,7798,8208,7164,10080,8208,8064,10560,8568,10068
%N A029713 Theta series of 6-dimensional 8-modular lattice of minimal norm 4.
%D A029713 M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 
               147-157. MR0805086 (87e:11060)
%H A029713 G. Nebe and N. J. A. Sloane, <a href="http://www.research.att.com/~njas/
               lattices/6QF.6.d.html">Home page for this lattice</a>
%F A029713 Associated with permutations in Mathieu group M24 of shape (8)^2(4)(2)(1)^2.
%F A029713 G.f. is Fourier series of a weight 3 level 8 modular form. f(-1/ (8 t)) 
               = (512)^(1/2) (t/i)^3 f(t) where q = exp(2 pi i t).
%e A029713 1 + 30*q^4 + 56*q^6 + 66*q^8 + 144*q^10 + 188*q^12 + 288*q^14 + ...
%o A029713 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ( eta(x^2 
               + A) * eta(x^4 + A) )^9 / ( eta(x + A) * eta(x^8 + A) )^6 -6 * x 
               * ( eta(x + A) * eta(x^8 + A) )^2 * eta(x^2 + A) * eta(x^4 + A), 
               n))} /* Michael Somos Nov 24 2007 */
%o A029713 (PARI) {a(n) = if( n<0, 0, polcoeff( 1 + 2 * x * Ser(qfrep( [4, 1, -1, 
               -1, 1, -1; 1, 4, 0, 1, 2, 1; -1, 0, 4, -1, 2, -1; -1, 1, -1, 4, -1, 
               0; 1, 2, 2, -1, 4, -1; -1, 1, -1, 0, -1, 4], n, 1)), n))} /* Michael 
               Somos Nov 24 2007 */
%Y A029713 Sequence in context: A043952 A006315 A027578 this_sequence A154599 A031126 
               A048451
%Y A029713 Adjacent sequences: A029710 A029711 A029712 this_sequence A029714 A029715 
               A029716
%K A029713 nonn
%O A029713 0,3
%A A029713 N. J. A. Sloane (njas(AT)research.att.com).

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