A063110 Dimension of the space of weight 2n cusp forms for Gamma_0(42).

5, 20, 36, 52, 68, 84, 100, 116, 132, 148, 164, 180, 196, 212, 228, 244, 260, 276, 292, 308, 324, 340, 356, 372, 388, 404, 420, 436, 452, 468, 484, 500, 516, 532, 548, 564, 580, 596, 612, 628, 644, 660, 676, 692, 708, 724, 740, 756, 772, 788

Offset

1,1

Comments

Except for initial term is same as n such Mod(2*fibonacci(n)+1,7)=0 - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 29 2004

From Michael Somos, May 29 2013: (Start)

Dimension of the space of weight n+1 cusp forms for Gamma_1(24).

Dimension of the space of weight 2n+1 cusp forms for Gamma_0(42) is 0. (End)

Links

Table of n, a(n) for n=1..50.

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

William A. Stein, The modular forms database

Formula

Conjecture: a(n) = 16*n-12 for n>1. a(n) = 2*a(n-1)-a(n-2) for n>3. G.f.: x*(5+10*x+x^2)/(1-x)^2. - Colin Barker, Sep 23 2012

Prog

(PARI) {a(n) = if( n<2, 5*(n==1), 16*n - 12)}; /* Michael Somos, May 29 2013 */
(Sage) def a(n) : return( len( CuspForms( Gamma1( 24), n+1, prec = 1). basis())); # Michael Somos, May 29 2013

Crossrefs

Sequence in context: A047716 A344190 A326005 * A044066 A013337 A031082

Adjacent sequences: A063107 A063108 A063109 * A063111 A063112 A063113

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2001

Status

approved