Search: id:A115155
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%I A115155
%S A115155 1,1,3,3,5,3,0,7,9,5,0,9,0,0,15,5,14,9,22,15,0,0,34,21,25,0,27,0,0,15,
               2,
%T A115155 33,0,14,0,27,0,22,0,35,0,0,0,0,45,34,14,15,49,25,42,0,86,27,0,0,66,0,
               0,
%U A115155 45,118,2,0,13,0,0,0,42,102,0,0,63,0,0,75,66,0,0,98,25,81,0,154,0
%V A115155 1,1,-3,-3,5,-3,0,-7,9,5,0,9,0,0,-15,5,-14,9,-22,-15,0,0,34,21,25,0,-27,
               0,0,-15,2,33,0,
%W A115155 -14,0,-27,0,-22,0,-35,0,0,0,0,45,34,-14,-15,49,25,42,0,-86,-27,0,0,66,
               0,0,45,-118,2,0,
%X A115155 13,0,0,0,42,-102,0,0,-63,0,0,-75,66,0,0,98,25,81,0,154,0
%N A115155 Expansion of a newform level 15 weight 3 and nontrivial character.
%H A115155 S. R. Finch, <a href="http://algo.inria.fr/csolve/frs.pdf">Modular Forms 
               on SL_2(Z)</a>. see page 5
%H A115155 W. Stein, <a href="http://modular.fas.harvard.edu:8080/mfd/space.html?space=[15,
               %203,%20[1,%202]]&search=15">Modular Forms Database</a>.
%F A115155 a(n) is multiplicative with a(3^e) = (-3)^e, a(5^e) = 5^e, a(p^e) = p^e 
               if e even else 0 if p == 7, 11, 13, 14 (mod 15), a(p^e) = a(p)a(p^(e-1)) 
               -p^2*a(p^(e-2)) if p == 1, 2, 4, 8 (mod 15).
%F A115155 Expansion of (eta(q^3)eta(q^5))^3+(eta(q)eta(q^15))^3 in powers of q.
%e A115155 q +q^2 - 3*q^3 - 3*q^4 +5*q^5 - 3*q^6 - 7*q^8 +9*q^9 +5*q^10 +...
%o A115155 (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x^3+A)*eta(x^5+A))^3+x*(eta(x+A)*eta(x^15+A\
               ))^3, n))}
%Y A115155 A106853(n)=a(2^n).
%Y A115155 Sequence in context: A142961 A101777 A016555 this_sequence A136549 A077924 
               A003569
%Y A115155 Adjacent sequences: A115152 A115153 A115154 this_sequence A115156 A115157 
               A115158
%K A115155 sign,mult
%O A115155 1,3
%A A115155 Michael Somos, Jan 14 2006

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