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

1,11

Comments

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)

Links

Table of n, a(n) for n=1..85.

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.

MAGMA Calculator.

Prog

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

Crossrefs

Cf. A159630, A159631, A159633, A159635, A159636 [From Steven Finch, Apr 22 2009]

Sequence in context: A103615 A308167 A293665 * A164733 A288311 A244366

Adjacent sequences: A159629 A159630 A159631 * A159633 A159634 A159635

Keyword

nonn

Author

Steven Finch, Apr 17 2009

Status

approved