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A159631 Dimension of space of modular forms of weight 1/2, level 4*n and trivial character. 4


%S 1,1,1,2,1,1,1,2,2,1,1,2,1,1,1,3,1,2,1,2,1,1,1,2,2,1,2,2,1,1,1,3,1,1,

%T 1,4,1,1,1,2,1,1,1,2,2,1,1,3,2,2,1,2,1,2,1,2,1,1,1,2,1,1,2,4,1,1,1,2,

%U 1,1,1,4,1,1,2,2,1,1,1,3,3,1,1,2,1,1,1,2,1,2,1,2,1,1,1,3,1,2,2,4,1,1,1,2,1,1,1,4,1,1,1,3,1,1,1,2,2,1,1,2,2,1,1,2,3

%N Dimension of space of modular forms of weight 1/2, level 4*n and trivial character.

%C We have a(n) = A046951(n) for all n < 125, but a(125)=3 > 2=A046951(125).

%C Also, the first nonzero cusp form of weight 1/2 occurs at level 1728.

%H Antti Karttunen, <a href="/A159631/b159631.txt">Table of n, a(n) for n = 1..1200</a>

%H H. Cohen and J. Oesterle, <a href="http://dx.doi.org/10.1007/BFb0065297">Dimensions des espaces de formes modulaires</a>, Modular Functions of One Variable. VI, Proc. 1976 Bonn conf., Lect. Notes in Math. 627, Springer-Verlag, 1977, pp. 69-78.

%H <a href="http://magma.maths.usyd.edu.au/calc/">MAGMA Calculator</a>.

%o (MAGMA) [[4*n,Dimension(HalfIntegralWeightForms(4*n,1/2))] : n in [1..125]]

%o (MAGMA) function a(n) return Dimension( ModularForms( Gamma0(4*n), 1/2)); end function; /* _Michael Somos_, Jun 13 2014 */

%Y Cf. A046951.

%K nonn

%O 1,4

%A _Steven Finch_, Apr 17 2009

%E Data section filled up to 125 terms by _Antti Karttunen_, Jul 23 2017

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Last modified April 21 11:10 EDT 2021. Contains 343150 sequences. (Running on oeis4.)