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