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A159632 Dimension of space of cusp forms of weight 3/2, level 4*n and trivial character. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 07:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)