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%I #10 Sep 08 2022 08:45:44
%S 0,0,0,0,0,0,1,0,0,1,2,0,2,2,3,1,3,2,4,2,5,4,5,2,2,5,5,4,6,7,7,3,9,7,
%T 9,4,8,8,11,6,9,11,10,8,10,10,11,7,6,8,15,10,12,11,15,10,17,13,14,14,
%U 14,14,18,8,17,19,16,14,21,19,17,12,17,17,20,16,21,23,19,15,15,19,20,22,23
%N Dimension of space of cusp forms of weight 3/2, level 4*n and trivial character.
%C Contribution from _Steven Finch_, Apr 22 2009: (Start)
%C Denote dim{M_k(Gamma_0(N))} by m(k,N) and dim{S_k(Gamma_0(N))} by s(k,N).
%C We have
%C m(3/2,N)-s(3/2,N)+m(1/2,N)-s(1/2,N) = m(5/2,N)-s(5/2,N)
%C hence
%C s(3/2,N)+s(1/2,N) = m(1/2,N)+m(3/2,N)-(m(5/2,N)-s(5/2,N))
%C = A159631(N/4)+A159630(N/4)-A159633(N/4)
%C where N is any positive multiple of 4. (End)
%H H. Cohen and J. Oesterle, <a href="http://dx.doi.org/10.1007/BFb0065297">Dimensions des espaces de formes modulaires</a>, Modular Functions of One Variable. VI, Proc. 1976 Bonn conf., Lect. Notes in Math. 627, Springer-Verlag, 1977, pp. 69-78.
%H <a href="http://magma.maths.usyd.edu.au/calc/">MAGMA Calculator</a>.
%o (Magma) [[4*n,Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n,3/2)))] : n in [1..90]]
%Y Cf. A159630, A159631, A159633, A159635, A159636 [From _Steven Finch_, Apr 22 2009]
%K nonn
%O 1,11
%A _Steven Finch_, Apr 17 2009