A159633 -id:A159633 - cp's OEIS frontend

A159632 Dimension of space of cusp forms of weight 3/2, level 4*n and trivial character.

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, 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, 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

Offset: 1

Steven Finch, Apr 17 2009

nonn

Contribution from Steven Finch, Apr 22 2009: (Start)
Denote dim{M_k(Gamma_0(N))} by m(k,N) and dim{S_k(Gamma_0(N))} by s(k,N).
We have
m(3/2,N)-s(3/2,N)+m(1/2,N)-s(1/2,N) = m(5/2,N)-s(5/2,N)
hence
s(3/2,N)+s(1/2,N) = m(1/2,N)+m(3/2,N)-(m(5/2,N)-s(5/2,N))
= A159631(N/4)+A159630(N/4)-A159633(N/4)
where N is any positive multiple of 4. (End)

H. Cohen and J. Oesterle, Dimensions des espaces de formes modulaires, Modular Functions of One Variable. VI, Proc. 1976 Bonn conf., Lect. Notes in Math. 627, Springer-Verlag, 1977, pp. 69-78.
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Cf. A159630, A159631, A159633, A159635, A159636 [From Steven Finch, Apr 22 2009]

[[4*n,Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n,3/2)))] : n in [1..90]];

cp's OEIS Frontend

A159632 Dimension of space of cusp forms of weight 3/2, level 4*n and trivial character.

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