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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)