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A063289 Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ). 1

%I

%S -1,2,7,11,16,20,25,29,34,38,43,47,52,56,61,65,70,74,79,83,88,92,97,

%T 101,106,110,115,119,124,128,133,137,142,146,151,155,160,164,169,173,

%U 178,182,187,191,196,200,205,209,214,218,223,227,232,236

%N Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).

%C It appears that for n > 2 a(n) = floor((9n-22)/2). - _Gary Detlefs_, Mar 02 2010

%H William A. Stein, <a href="http://wstein.org/Tables/dimskg1new.gp">Dimensions of the spaces S_k^{new}(Gamma_1(N))</a>

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

%F Conjecture: a(n) = 9*n/4 + (-1)^n/4 - 45/4 for n >= 3, with first differences in A010710. - _R. J. Mathar_, Dec 06 2010

%F Conjectures from _M. F. Hasler_, Mar 05 2012: (Start)

%F G.f.: x^2*(-1 + 3*x + 6*x^2 + x^3)/(1 - x - x^2 + x^3).

%F a(n+2) = a(n)+9 (n>2), a(2n+1) = a(2n)+4 (n>1), a(2n) = a(2n-1)+5 (n>1). (End)

%Y Cf. A063232, A063233.

%K sign

%O 2,2

%A _N. J. A. Sloane_, Jul 14 2001

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Last modified June 12 06:39 EDT 2021. Contains 344943 sequences. (Running on oeis4.)