A063118 Dimension of the space of weight 2n cusp forms for Gamma_0(50).

2, 17, 31, 47, 61, 77, 91, 107, 121, 137, 151, 167, 181, 197, 211, 227, 241, 257, 271, 287, 301, 317, 331, 347, 361, 377, 391, 407, 421, 437, 451, 467, 481, 497, 511, 527, 541, 557, 571, 587, 601, 617, 631, 647, 661, 677, 691, 707, 721, 737, 751, 767, 781

Offset

1,1

Comments

Appears to agree with the first 11-section of A186042 except for the first term of both sequences (verified up to a(10000)). - Klaus Brockhaus, Mar 10 2011

Links

Klaus Brockhaus, Table of n, a(n) for n = 1..10000

William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).

William A. Stein, The modular forms database

Formula

From Klaus Brockhaus, Mar 10 2011: (Start)

G.f. (conjectured): x*(x^3 + 12*x^2 + 15*x + 2) / ((x - 1)^2*(x + 1)).

Recurrences (conjectured):

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

a(n) = a(n-2) + 30 for n > 3. (End)

Closed formula (conjectured): a(n) = (30*n+(-1)^n-27)/2 for n > 1. - Bruno Berselli, Mar 10 2011

Recurrence (conjectured): a(n) = 2*a(n-1) -a(n-2) +2*(-1)^n, n > 3. - Vincenzo Librandi, Mar 24 2011

Conjecture: a(n) = A007775(4*n - 3), n > 1. - Bill McEachen, May 15 2022

Example

G.f. = 2*x + 17*x^2 + 31*x^3 + 47*x^4 + 61*x^5 + 77*x^6 + 91*x^7 + 107*x^8 + 121*x^9 + ...

Prog

(Magma) [ Dimension(CuspForms(Gamma0(50), 2*n)): n in [1..55] ]; // Klaus Brockhaus, Mar 10 2011
(Sage) def a(n) : return( len( CuspForms( Gamma0( 50), 2*n, prec=1) . basis())); # Michael Somos, May 29 2013

Crossrefs

Cf. A186042, A007775.

Sequence in context: A139827 A362035 A197186 * A267540 A141068 A162622

Adjacent sequences: A063115 A063116 A063117 * A063119 A063120 A063121

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2001

Status

approved