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A127788
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Dimension of the space of newforms of weight 2 and level n.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 1, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 1, 1, 1, 4, 1, 1, 2, 3, 1, 4, 2, 3, 2, 3, 2, 5, 0, 4, 3, 3, 1, 5, 3, 5, 2, 3, 1, 6, 1, 5, 4, 3, 1, 5, 1, 6, 2, 2, 3, 7, 2, 5, 4, 5, 3, 7, 3, 7, 2, 5, 3, 7, 2, 7, 3, 4, 1, 8, 3
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OFFSET
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1,23
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COMMENTS
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"Newform" is meant in the sense of Atkin-Lehner, that is, a primitive Hecke eigenform relative to the subgroup Gamma_0 (n)
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REFERENCES
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E. Halberstadt and A. Kraus, Courbes de Fermat: resultats et problemes, J. Reine Angew. Math. 548 (2002) 167-234. [From Steven Finch, Mar 27 2009]
G. Martin, Dimensions of the spaces of cusp forms and newforms on Gamma0(N) and Gamma1(N), J. Number Theory 112 (2005) 298-331. [From Steven Finch, Mar 27 2009]
H. Cohen, Number Theory. Vol. II. Analytic and Modern Tools. Springer, 2007, pp. 496-497. [From Steven Finch, Mar 27 2009]
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LINKS
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Table of n, a(n) for n=1..102.
Formula (5.8) in Xian-Jin Li, An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials, J. Number Theory 113 (2005) 175-200
Table A in Toshitsune Miyake, Modular Forms, Springer-Verlag, 1989
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FORMULA
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a(n) = A001617(n) - sum a(m)*d(n/m), where the summation is over all divisors 1 < m < n of n and d is the divisor function
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EXAMPLE
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a(p) = A001617(p) for any prime p
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CROSSREFS
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Cf. A001617, A116563.
Sequence in context: A025854 A190766 A025857 * A025656 A194517 A110658
Adjacent sequences: A127785 A127786 A127787 * A127789 A127790 A127791
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KEYWORD
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nonn
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AUTHOR
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Steven Finch, Apr 04 2007
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STATUS
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approved
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