%I #13 Aug 22 2019 12:18:12

%S -1,7,21,36,51,66,81,96,111,126,141,154,171,186,201,214,231,244,261,

%T 274,291,304,321,332,351,364,381,392,411,422,441,452,471,482,501,510,

%U 531,542,561,570,591,600,621,630,651,660,681,688,711,720

%N Dimension of the space of weight n cuspidal newforms for Gamma_1( 19 ).

%H William A. Stein, <a href="http://wstein.org/Tables/dimskg1new.gp">Dimensions of the spaces S_k^{new}(Gamma_1(N))</a>

%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>

%F Conjectures from _Colin Barker_, Feb 24 2016: (Start)

%F a(n) = a(n-4) + a(n-6) - a(n-10) for n>13.

%F G.f.: -x^2*(1 -7*x -21*x^2 -36*x^3 -52*x^4 -59*x^5 -61*x^6 -53*x^7 -39*x^8 -24*x^9 -8*x^10 +x^11) / ((1 -x)^2*(1 +x)^2*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)). (End)

%K sign

%O 2,2

%A _N. J. A. Sloane_, Jul 14 2001