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Search: id:A159632
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| A159632 |
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Dimension of space of cusp forms of weight 3/2, level 4*n and trivial character. |
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+0
2
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| 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; listen)
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OFFSET
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1,11
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COMMENT
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Contribution from S. R. Finch (Steven.Finch(AT)inria.fr), 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)
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REFERENCES
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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
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Magma Calculator.
Scanned copy of Cohen-Oesterle.
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PROGRAM
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(MAGMA) [[4*n, Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 3/2)))] : n in [1..90]]
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CROSSREFS
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A159630, A159631, A159633, A159635, A159636 [From S. R. Finch (Steven.Finch(AT)inria.fr), Apr 22 2009]
Sequence in context: A061199 A144741 A103615 this_sequence A164733 A070101 A022830
Adjacent sequences: A159629 A159630 A159631 this_sequence A159633 A159634 A159635
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KEYWORD
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nonn
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AUTHOR
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S. R. Finch (Steven.Finch(AT)inria.fr), Apr 17 2009
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