A063206 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 31 ).

2, 7, 13, 17, 23, 27, 33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, 87, 93, 97, 103, 107, 113, 117, 123, 127, 133, 137, 143, 147, 153, 157, 163, 167, 173, 177, 183, 187, 193, 197, 203, 207, 213, 217, 223, 227, 233, 237, 243, 247

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn

Comments

The terms obey a(n)=10*(n-1)-a(n-1), n>2 as far as tabulated, [Vincenzo Librandi, Dec 07 2010, corrected by R. J. Mathar, Dec 07 2010]

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 (1,1,-1).

Formula

From Colin Barker, Oct 16 2014: (Start)

a(n) = -5/2-(-1)^n/2+5*n for n>1.

a(n) = a(n-1)+a(n-2)-a(n-3) for n>4.

G.f.: -x*(x^3-4*x^2-5*x-2) / ((x-1)^2*(x+1)).

(End)