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Search: id:A136549
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| A136549 |
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Expansion of a newform level 15 weight 3 and nontrivial character. |
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+0
1
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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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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 * (1 + (-1)^e) / 2 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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See A115155 for another version of the same sequence.
Adjacent sequences: A136546 A136547 A136548 this_sequence A136550 A136551 A136552
Sequence in context: A101777 A016555 A115155 this_sequence A077924 A003569 A066670
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KEYWORD
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sign,mult
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AUTHOR
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Michael Somos, Jan 05 2008
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