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Dimension of the space of weight 2n cusp forms for Gamma_0( 19 ).
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%I #13 Aug 22 2019 12:18:12

%S 1,4,8,10,14,18,20,24,28,30,34,38,40,44,48,50,54,58,60,64,68,70,74,78,

%T 80,84,88,90,94,98,100,104,108,110,114,118,120,124,128,130,134,138,

%U 140,144,148,150,154,158,160,164

%N Dimension of the space of weight 2n cusp forms for Gamma_0( 19 ).

%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.

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

%F Conjecture: a(n) = 4*(n-1)-2*floor((n-1)/3) for n > 1. - _Wesley Ivan Hurt_, Dec 27 2016

%F Conjectures from _Colin Barker_, Jun 09 2019: (Start)

%F G.f.: x*(1 + 3*x + 4*x^2 + x^3 + x^4) / ((1 - x)^2*(1 + x + x^2)).

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>5.

%F (End)

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jul 08 2001