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Search: id:A115155
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| A115155 |
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Expansion of a newform level 15 weight 3 and nontrivial character. |
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+0
2
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| 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, -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, 13, 0, 0, 0, 42, -102, 0, 0, -63, 0, 0, -75, 66, 0, 0, 98, 25, 81, 0, 154, 0
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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S. R. Finch, Modular Forms on SL_2(Z). see page 5
W. Stein, Modular Forms Database.
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FORMULA
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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).
Expansion of (eta(q^3)eta(q^5))^3+(eta(q)eta(q^15))^3 in powers of q.
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EXAMPLE
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q +q^2 - 3*q^3 - 3*q^4 +5*q^5 - 3*q^6 - 7*q^8 +9*q^9 +5*q^10 +...
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PROGRAM
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(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))}
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CROSSREFS
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A106853(n)=a(2^n).
Sequence in context: A142961 A101777 A016555 this_sequence A136549 A077924 A003569
Adjacent sequences: A115152 A115153 A115154 this_sequence A115156 A115157 A115158
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Jan 14 2006
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