A063215 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 47 ).

4, 11, 19, 27, 35, 41, 51, 57, 65, 73, 81, 87, 97, 103, 111, 119, 127, 133, 143, 149, 157, 165, 173, 179, 189, 195, 203, 211, 219, 225, 235, 241, 249, 257, 265, 271, 281, 287, 295, 303, 311, 317, 327, 333, 341, 349, 357, 363, 373, 379

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn
• easy
• changed

Links

• William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))
• William A. Stein, The modular forms database
• Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1).

Programs

Mathematica

a[n_] := a[n] = If[n <= 6, {4, 11, 19, 27, 35, 41}[[n]], a[n-2] + a[n-3] - a[n-5]]; Array[a, 50] (* Jean-François Alcover, Dec 06 2016 after Colin Barker *)
LinearRecurrence[{0,1,1,0,-1},{4,11,19,27,35,41},50] (* Harvey P. Dale, Aug 25 2025 *)

PARI

a(n)=if(n>1, ([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; -1,0,1,1,0]^(n-1)*[5;11;19;27;35])[1,1], 4) \\ Charles R Greathouse IV, Nov 27 2016

Formula

a(n) = a(n-2)+a(n-3)-a(n-5) for n>6. G.f.: x*(4+11*x+15*x^2+12*x^3+5*x^4-x^5)/((1 -x)^2*(1 +x)*(1 +x +x^2)). - Colin Barker, Sep 27 2012