A063198 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 10 ).

0, 1, 3, 1, 3, 5, 3, 5, 7, 5, 7, 9, 7, 9, 11, 9, 11, 13, 11, 13, 15, 13, 15, 17, 15, 17, 19, 17, 19, 21, 19, 21, 23, 21, 23, 25, 23, 25, 27, 25, 27, 29, 27, 29, 31, 29, 31, 33, 31, 33

Offset

1,3

Comments

The dimension of weight n is apparently given by 0, 0, 2, 1, 0, 3, 2, 1, 4,... etc as in A063942. - R. J. Mathar, Jul 14 2015

Links

R. J. Mathar, Table of n, a(n) for n = 1..1000

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).

Formula

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

For n>1, a(n) = (6*n-3+12*cos(2*n*Pi/3)-4*sqrt(3)*sin(2*n*Pi/3))/9. - Wesley Ivan Hurt, Sep 30 2017

Crossrefs

Cf. A063942.

Sequence in context: A284130 A005474 A012264 * A122582 A173039 A016471

Adjacent sequences: A063195 A063196 A063197 * A063199 A063200 A063201

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 10 2001

Status

approved