A063233 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 79 ).

6, 19, 33, 45, 59, 71, 85, 97, 111, 123, 137, 149, 163, 175, 189, 201, 215, 227, 241, 253, 267, 279, 293, 305, 319, 331, 345, 357, 371, 383, 397, 409, 423, 435, 449, 461, 475, 487, 501, 513, 527, 539, 553, 565, 579, 591, 605, 617, 631, 643

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn

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).

Programs

Mathematica

Join[{6}, Table[13*n - (13 + (-1)^n)/2, {n, 2, 50}]] (* Amiram Eldar, Jan 12 2024 *)

Formula

Except for the first term, a(n) = 26*(n-1) - a(n-1) (with a(2)=19). - Vincenzo Librandi, Dec 07 2010

From M. F. Hasler, Mar 05 2012: (Start)

a(n+2) = a(n) + 26 (n > 1);

a(2n+1) = a(2n) + 14 (n > 0);

a(2n) = a(2n-1) + 12 (n > 1);

a(n) = 13n - { 6 if n = 2k+1, k > 0; 7 otherwise }.

G.f.: x*(6 + 13*x + 8*x^2 - x^3)/(1 - x - x^2 + x^3). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/42 + tan(3*Pi/13)*Pi/26 . - Amiram Eldar, Jan 12 2024