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A159634
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Coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4*n and trivial character, where k>=5 is odd.
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1
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1, 2, 4, 4, 6, 8, 8, 8, 12, 12, 12, 16, 14, 16, 24, 16, 18, 24, 20, 24, 32, 24, 24, 32, 30, 28, 36, 32, 30, 48, 32, 32, 48, 36, 48, 48, 38, 40, 56, 48, 42, 64, 44, 48, 72, 48, 48, 64, 56, 60, 72, 56, 54, 72, 72, 64, 80, 60, 60, 96, 62, 64, 96, 64, 84, 96, 68, 72, 96, 96
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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(7/2,N)+s(5/2,N) = m(5/2,N)+s(7/2,N) =
(m(11/2,N)+s(9/2,N))/2 = (m(9/2,N)+s(11/2,N))/2 =
(m(15/2,N)+s(13/2,N))/3 = (m(13/2,N)+s(15/2,N))/3 = ...
(m((4j+3)/2,N)+s((4j+1)/2,N))/j = (m((4j+1)/2,N)+s((4j+3)/2,N))/j = ...
where N is any positive multiple of 4 and j>=1.
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REFERENCES
| 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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LINKS
| Magma Calculator.
Scanned copy of Cohen-Oesterle.
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PROG
| (MAGMA) [[4*n, (Dimension(HalfIntegralWeightForms(4*n, 7/2))+Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2))))/2] : n in [1..70]]; [[4*n, (Dimension(HalfIntegralWeightForms(4*n, 5/2))+Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 7/2))))/2] : n in [1..70]];
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CROSSREFS
| Cf. A159635, A159636 [From S. R. Finch (Steven.Finch(AT)inria.fr), Apr 22 2009]
Sequence in context: A132118 A007843 A053196 * A186690 A002131 A063200
Adjacent sequences: A159631 A159632 A159633 * A159635 A159636 A159637
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KEYWORD
| nonn
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AUTHOR
| S. R. Finch (Steven.Finch(AT)inria.fr), Apr 17 2009
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