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

1,4

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.

Prog

(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 */

Crossrefs

Cf. A046951.

Sequence in context: A049419 A299090 A046951 * A368216 A335428 A368781

Adjacent sequences: A159628 A159629 A159630 * A159632 A159633 A159634

Keyword

nonn

Author

Steven Finch, Apr 17 2009

Extensions

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

Status

approved