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Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 9 ).
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%I #20 Oct 15 2020 21:21:11

%S 0,1,1,3,3,4,5,6,6,8,8,9,10,11,11,13,13,14,15,16,16,18,18,19,20,21,21,

%T 23,23,24,25,26,26,28,28,29,30,31,31,33,33,34,35,36,36,38,38,39,40,41

%N Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 9 ).

%H Michael De Vlieger, <a href="/A063197/b063197.txt">Table of n, a(n) for n = 1..10000</a>

%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(Gamma_0(N))</a>

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1).

%F From _Colin Barker_, Sep 27 2012: (Start)

%F a(n) = a(n-2) + a(n-3) - a(n-5) for n > 5.

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

%F (End)

%F a(n) = n-1 - floor((n-1)/2) + floor((n-1)/3). - _Ridouane Oudra_, Oct 15 2020

%t Rest@ CoefficientList[Series[x^2*(1 + x + 2*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 + x + x^2)), {x, 0, 69}], x] (* or *)

%t Array[# - Floor[#/2] + Floor[#/3] &[# - 1] &, 69] (* _Michael De Vlieger_, Oct 15 2020 *)

%o (PARI) concat(0, Vec(x^2*(1 +x +2*x^2 +x^3)/((1 -x)^2*(1 +x)*(1 +x +x^2)) + O(x^80))) \\ _Michel Marcus_, Oct 15 2020

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Jul 10 2001