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

%I A159636 #36 Aug 04 2025 20:53:33
%S A159636 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,
%T A159636 21,30,22,16,32,24,32,24,27,27,38,28,30,42,31,30,48,33,34,36,36,36,50,
%U A159636 36,39,45,50,40,56,42,43,60
%N A159636 Dimension of space of cusp forms of weight 5/2, level 4*n and trivial character.
%H A159636 G. C. Greubel, <a href="/A159636/b159636.txt">Table of n, a(n) for n = 1..10000</a>
%H A159636 H. Cohen and J. Oesterle, <a href="http://dx.doi.org/10.1007/BFb0065297">Dimensions des espaces de formes modulaires</a>, Modular Functions of One Variable. VI, Proc. 1976 Bonn conf., Lect. Notes in Math. 627, Springer-Verlag, 1977, pp. 69-78.
%H A159636 S. R. Finch, <a href="/A001616/a001616.pdf">Primitive Cusp Forms</a>, April 27, 2009. [Cached copy, with permission of the author]
%t A159636 dedekindPsi[n_Integer] := n*Times @@ (1 + 1/First /@ FactorInteger[n]);
%t A159636 \[Chi][n_Integer] := Sum[EulerPhi[GCD[d, n/d]], {d, Divisors[n]}];
%t A159636 r[(p_)?PrimeQ, n_Integer] := -1+ Last[Flatten[Cases[FactorInteger[p*n], {p, _}]]];
%t A159636 \[Alpha][n_Integer] := Block[{rn}, rn = r[2, n]; If[EvenQ[rn], 3*2^(rn/2 - 1), 2^(rn/2 + 1/2)]];
%t A159636 \[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]];
%t A159636 s[5/2, n_Integer] := (1/8)* dedekindPsi[n] - \[Beta][n]*(\[Chi][n]/2/\[Alpha][n]);
%t A159636 s[5/2, #] & /@ Range[4, 240, 4] (* _Wouter Meeussen_, cf. Finch reference, Mar 31 2014 *)
%o A159636 (Magma) [[4*n,Dimension(CuspidalSubspace(HalfIntegralWeightForms(4*n,5/2)))] : n in [1..75]];
%Y A159636 Cf. A159630, A159634.
%K A159636 nonn
%O A159636 1,5
%A A159636 _Steven Finch_, Apr 17 2009