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 A127788 Dimension of the space of newforms of weight 2 and level n. 1

%I

%S 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,

%T 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,

%U 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

%N Dimension of the space of newforms of weight 2 and level n.

%C "Newform" is meant in the sense of Atkin-Lehner, that is, a primitive Hecke eigenform relative to the subgroup Gamma_0 (n)

%D 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]

%D 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]

%D H. Cohen, Number Theory. Vol. II. Analytic and Modern Tools. Springer, 2007, pp. 496-497. [From _Steven Finch_, Mar 27 2009]

%H Formula (5.8) in Xian-Jin Li, <a href="http://arXiv.org/abs/math/0403148">An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials</a>, J. Number Theory 113 (2005) 175-200

%H Table A in Toshitsune Miyake, <a href="http://modular.math.washington.edu/scans/miyake_modular_forms_tables/">Modular Forms</a>, Springer-Verlag, 1989

%F 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

%e a(p) = A001617(p) for any prime p

%Y Cf. A001617, A116563.

%K nonn

%O 1,23

%A _Steven Finch_, Apr 04 2007

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