VOOZH about

URL: https://oeis.org/A159636

⇱ A159636 - OEIS

login
A159636
Dimension of space of cusp forms of weight 5/2, level 4*n and trivial character.
5
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
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
Sequence in context: A057937 A080216 A082924 * A023647 A332413 A239207
KEYWORD
nonn
AUTHOR
Steven Finch, Apr 17 2009
STATUS
approved