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A037946 Coefficients of unique normalized cusp form Delta_22 of weight 22 for full modular group. 6

%I

%S 1,-288,-128844,-2014208,21640950,37107072,-768078808,1184071680,

%T 6140423133,-6232593600,-94724929188,259518615552,-80621789794,

%U 221206696704,-2788306561800,3883087691776,3052282930002

%N Coefficients of unique normalized cusp form Delta_22 of weight 22 for full modular group.

%D G. Harder. "A Congruence Between a Siegel and an Elliptic Modular Form." The 1-2-3 of modular forms. Springer Berlin Heidelberg, 2008. 247-262.

%H Seiichi Manyama, <a href="/A037946/b037946.txt">Table of n, a(n) for n = 1..1000</a>

%H Fernando Q. GouvĂȘa, <a href="http://projecteuclid.org/euclid.em/1047920420">Non-ordinary primes: a story</a>, Experimental Mathematics, Volume 6, Issue 3 (1997), 195-205.

%H S. C. Milne, <a href="https://arxiv.org/abs/math/0009130">Hankel determinants of Eisenstein series</a>, preprint, arXiv:0009130 [math.NT], 2000.

%H <a href="/index/Gre#groups_modular">Index entries for sequences related to modular groups</a>

%F a(n) == A013969(n) mod 77683. - _Seiichi Manyama_, Feb 03 2017

%F G.f.: (E_4(q)^3 - E_6(q)^2)/12^3 * E_4(q) * E_6(q). - _Seiichi Manyama_, Jun 09 2017

%F G.f.: 691/(1728*250) * (E_8(q)*E_14(q) - E_10(q)*E_12(q)). - _Seiichi Manyama_, Jul 25 2017

%e q^2 - 288*q^4 - ...

%t terms = 17;

%t E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];

%t E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];

%t ((E4[x]^3 - E6[x]^2)/12^3)*E4[x]*E6[x] + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* _Jean-François Alcover_, Feb 27 2018, after _Seiichi Manyama_ *)

%Y Cf. A000594 ((E_4(q)^3 - E_6(q)^2)/12^3), A004009 (E_4(q)), A013969, A013973 (E_6(q)), A290181.

%K sign

%O 1,2

%A _N. J. A. Sloane_

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Last modified November 11 18:50 EST 2019. Contains 329031 sequences. (Running on oeis4.)