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Search: id:A029713
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| A029713 |
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Theta series of 6-dimensional 8-modular lattice of minimal norm 4. |
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+0
3
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| 1, 0, 30, 56, 66, 144, 188, 288, 378, 448, 528, 504, 884, 1008, 1056, 1440, 1290, 1344, 1834, 1848, 2064, 2880, 2652, 3168, 3332, 2688, 3696, 3696, 4128, 5040, 5280, 5760, 5610, 5824, 6012, 5376, 7798, 8208, 7164, 10080, 8208, 8064, 10560, 8568, 10068
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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M. Koike, Matheiu group M24 and modular forms, Nagoya Math. J., 99 (1985), 147-157. MR0805086 (87e:11060)
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LINKS
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G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
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Associated with permutations in Mathieu group M24 of shape (8)^2(4)(2)(1)^2.
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).
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EXAMPLE
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1 + 30*q^4 + 56*q^6 + 66*q^8 + 144*q^10 + 188*q^12 + 288*q^14 + ...
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PROGRAM
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(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 */
(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 */
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CROSSREFS
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Adjacent sequences: A029710 A029711 A029712 this_sequence A029714 A029715 A029716
Sequence in context: A043952 A006315 A027578 this_sequence A154599 A031126 A048451
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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