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

1, -288, -128844, -2014208, 21640950, 37107072, -768078808, 1184071680, 6140423133, -6232593600, -94724929188, 259518615552, -80621789794, 221206696704, -2788306561800, 3883087691776, 3052282930002

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

Examples

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

References

• 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.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Fernando Q. Gouvêa, Non-ordinary primes: a story, Experimental Mathematics, Volume 6, Issue 3 (1997), 195-205.
• S. C. Milne, Hankel determinants of Eisenstein series, preprint, arXiv:0009130 [math.NT], 2000.
• Index entries for sequences related to modular groups

Crossrefs

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

Programs

Mathematica

terms = 17;
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms+1}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms+1}];
((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 *)

Formula

a(n) == A013969(n) mod 77683. - Seiichi Manyama, Feb 03 2017

G.f.: (E_4(q)^3 - E_6(q)^2)/12^3 * E_4(q) * E_6(q). - Seiichi Manyama, Jun 09 2017

G.f.: 691/(1728*250) * (E_8(q)*E_14(q) - E_10(q)*E_12(q)). - Seiichi Manyama, Jul 25 2017