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

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, 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, 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

Offset: 1

Author

Steven Finch, Apr 17 2009

Keywords

• nonn

Comments

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1200
• 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.
• MAGMA Calculator.

Crossrefs

Cf. A046951.

Programs

Magma

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

Magma

function a(n) return Dimension( ModularForms( Gamma0(4*n), 1/2)); end function; /* Michael Somos, Jun 13 2014 */

Extensions

Data section filled up to 125 terms by Antti Karttunen, Jul 23 2017