A063110 - OEIS

%I #19 Aug 22 2019 12:18:12

%S 5,20,36,52,68,84,100,116,132,148,164,180,196,212,228,244,260,276,292,

%T 308,324,340,356,372,388,404,420,436,452,468,484,500,516,532,548,564,

%U 580,596,612,628,644,660,676,692,708,724,740,756,772,788

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

%C 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

%C From _Michael Somos_, May 29 2013: (Start)

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

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

%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.

%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>

%F 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

%o (PARI) {a(n) = if( n<2, 5*(n==1), 16*n - 12)}; /* _Michael Somos_, May 29 2013 */

%o (Sage) def a(n) : return( len( CuspForms( Gamma1( 24), n+1, prec = 1). basis())); # _Michael Somos_, May 29 2013

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 08 2001