A159636 Dimension of space of cusp forms of weight 5/2, level 4*n and trivial character.

0, 0, 1, 0, 3, 3, 4, 2, 6, 6, 7, 6, 9, 9, 14, 6, 12, 12, 13, 12, 20, 15, 16, 16, 18, 18, 21, 18, 21, 30, 22, 16, 32, 24, 32, 24, 27, 27, 38, 28, 30, 42, 31, 30, 48, 33, 34, 36, 36, 36, 50, 36, 39, 45, 50, 40, 56, 42, 43, 60

Offset

1,5

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

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.

S. R. Finch, Primitive Cusp Forms, April 27, 2009. [Cached copy, with permission of the author]

Mathematica

dedekindPsi[n_Integer] := n*Times @@ (1 + 1/First /@ FactorInteger[n]);
\[Chi][n_Integer] := Sum[EulerPhi[GCD[d, n/d]], {d, Divisors[n]}];
r[(p_)?PrimeQ, n_Integer] := -1+ Last[Flatten[Cases[FactorInteger[p*n], {p, _}]]];
\[Alpha][n_Integer] := Block[{rn}, rn = r[2, n]; If[EvenQ[rn], 3*2^(rn/2 - 1), 2^(rn/2 + 1/2)]];
\[Beta][n_Integer] := Block[{rn}, rn = r[2, n]; Which[rn >= 4, \[Alpha][n], rn === 3, 3, rn === 2 && Or @@ OddQ[(r[#1, n] & ) /@ Select[First /@ FactorInteger[n], Mod[#1, 4] === 3 & ]], 2, True, 3/2]];
s[5/2, n_Integer] := (1/8)* dedekindPsi[n] - \[Beta][n]*(\[Chi][n]/2/\[Alpha][n]);
s[5/2, #] & /@ Range[4, 240, 4] (* Wouter Meeussen, cf. Finch reference, Mar 31 2014 *)

Prog

(Magma) [[4*n, Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n, 5/2)))] : n in [1..75]]

Crossrefs

Cf. A159630, A159634.

Sequence in context: A057937 A080216 A082924 * A023647 A332413 A239207

Adjacent sequences: A159633 A159634 A159635 * A159637 A159638 A159639

Keyword

nonn

Author

Steven Finch, Apr 17 2009

Status

approved