A063241 Dimension of the space of weight 2n cuspidal newforms for Gamma_0(90).

3, 5, 7, 13, 15, 17, 23, 25, 27, 33, 35, 37, 43, 45, 47, 53, 55, 57, 63, 65, 67, 73, 75, 77, 83, 85, 87, 93, 95, 97, 103, 105, 107, 113, 115, 117, 123, 125, 127, 133, 135, 137, 143, 145, 147, 153, 155, 157, 163, 165

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn
• easy

Comments

The sequence lists the odd numbers ending with 3, 5 and 7. This follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016

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 (1,0,1,-1).

Crossrefs

Cf. A063213.

Formula

G.f.: 3*x -x^2*(-5-2*x-6*x^2+3*x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 15 2015

a(n) = 2*n + 4*floor(n/3 - 1/3) + 1. This formula follows from Mathar's generating function. - Bruno Berselli, Feb 16 2016