Search: id:A129666
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%I A129666
%S A129666 1,1,2,7,16,2,7,15,23,16,8,14,28,7,32,41,54,23,110,112,14,8,48,30,131,
%T A129666 28,100,49,110,32,12,161,16,54,112,161,246,110,56,240,182,14,128,56,368,
%U A129666 48,324,82,49,131,108,196,162,100,128,105,220,110,810,224,488,12
%V A129666 1,-1,-2,-7,16,2,-7,15,-23,-16,-8,14,28,7,-32,41,54,23,-110,-112,14,8,
               48,-30,131,-28,
%W A129666 100,49,-110,32,12,-161,16,-54,-112,161,-246,110,-56,240,182,-14,128,56,
               -368,-48,324,
%X A129666 -82,49,-131,-108,-196,-162,-100,-128,-105,220,110,810,224,-488,-12
%N A129666 Expansion of unique cusp form of weight 4 level 7 in powers of q.
%D A129666 H. Rosson, G. Tornaria, Central values of quadratic twists for a modular 
               form of weight 4, pp. 315-321 of J. B. Conrey, et. al.,ed., Ranks 
               of Elliptic Curves and Random Matrix Theory, Cambridge University 
               Press, 2007..
%F A129666 Expansion of q * phi(-q)^3 * psi(q) * phi(-q^7)^3 * psi(q^7) + 4*q^2 
               * (phi(-q) * psi(q) * phi(-q^7) * psi(q^7))^2 in powers of q.
%F A129666 Expansion of ((eta(q) * eta(q^7))^3 +4 * (eta(q^2) * eta(q^14))^3) * 
               (eta(q) * eta(q^7))^2/ (eta(q^2) * eta(q^14)) in powers of q.
%F A129666 a(n) is multiplicative with a(7^e) = (-7)^e, a(p^e) = a(p)*a(p^(e-1)) 
               -p^3*a(p^(e-2)).
%F A129666 G.f. is Fourier series of a weight 4 level 7 cusp form. f(-1/ (7 t)) 
               = 49 t^4 f(t) where q = exp(2 pi i t) .
%F A129666 G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^4)) where f(u, v, w) = (u^2 
               + 2*u*v + 16*u*w + 12*v^2 + 32*v*w + 256*w^2)*(-v^3 + 2*w*u*v + w*u^2 
               + 16*w^2*u) +2*v^5.
%e A129666 q - q^2 - 2*q^3 - 7*q^4 + 16*q^5 + 2*q^6 - 7*q^7 + 15*q^8 - 23*q^9 - 
               ...
%o A129666 (PARI) {a(n)= local(A, A1, A2); if(n<1, 0, n--; A= x*O(x^n); A1= eta(x+A)* 
               eta(x^7+A); A2= eta(x^2+A)* eta(x^14+A); polcoeff( (A1^3 +4*x*A2^3)* 
               A1^2/A2, n))}
%Y A129666 Convolution of A002652 and A002656.
%Y A129666 Sequence in context: A050612 A120110 A047694 this_sequence A135781 A167236 
               A041573
%Y A129666 Adjacent sequences: A129663 A129664 A129665 this_sequence A129667 A129668 
               A129669
%K A129666 sign,mult
%O A129666 1,3
%A A129666 Michael Somos, Apr 27 2007

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