A063213 Dimension of the space of weight 2n cuspidal newforms for Gamma_0(45).

1, 5, 9, 11, 15, 19, 21, 25, 29, 31, 35, 39, 41, 45, 49, 51, 55, 59, 61, 65, 69, 71, 75, 79, 81, 85, 89, 91, 95, 99, 101, 105, 109, 111, 115, 119, 121, 125, 129, 131, 135, 139, 141, 145, 149, 151, 155, 159, 161, 165

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn
• easy

Comments

The sequence lists the odd numbers ending with 1, 5 and 9. 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. A063241.

Formula

G.f.: x - x^2*(-5-4*x-2*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 15 2015

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