A037947 Coefficients of unique normalized cusp form Delta_26 of weight 26 for full modular group.

1, -48, -195804, -33552128, -741989850, 9398592, 39080597192, 3221114880, -808949403027, 35615512800, 8419515299052, 6569640870912, -81651045335314, -1875868665216, 145284580589400, 1125667983917056, -2519900028948078

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

Examples

			q^2 - 48*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)), A013973 (E_6(q)), A290182.

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)*E6[x]*E4[x]^2 + O[x]^(terms+1) // CoefficientList[#, x]& // Rest (* Jean-François Alcover, Feb 27 2018, after Seiichi Manyama *)

Formula

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

G.f.: -691*3617/(1728*2*3*5^3*7^2*13) * (E_10(q)*E_16(q) - E_12(q)*E_14(q)). - Seiichi Manyama, Jul 25 2017