%I #14 May 02 2023 13:13:12

%S -1,39,92,143,194,249,300,351,406,457,508,561,614,665,720,769,822,875,

%T 928,977,1034,1083,1136,1187,1242,1291,1348,1395,1450,1501,1556,1603,

%U 1662,1709,1764,1813,1870,1917,1976,2021,2078,2127,2184

%N Dimension of the space of weight n cuspidal newforms for Gamma_1( 45 ).

%C Conjecture: satisfies a linear recurrence having signature (0, 0, 0, 1, 0, 1, 0, 0, 0, -1). - _Harvey P. Dale_, Jul 07 2021

%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 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 -39*x -92*x^2 -143*x^3 -195*x^4 -210*x^5 -209*x^6 -169*x^7 -120*x^8 -65*x^9 -13*x^10) / ((1 -x)^2*(1 +x)^2*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)).

%F (End)

%K sign

%O 2,2

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