Manipulate[If[Abs[m] > l, m = Sign[m] l];
 coloredSphere[l, m, reim, ControlActive[30, pp]],
 {{reim, Re, "view"}, {Re -> "real", Im -> "imaginary"}},
 {{l, 6, "l"}, 0, 12, 1},
 {{m, 3, "m"}, -l, l, 1},
 {{pp, 40, "points"}, 3, 50, 1},
 Initialization :>
  {makeColoredSphereGraphicsComplex[points_, normals_, colors_] :=
    Module[{lOuter = Length[points], lInner = Length[points[[1]]]},
     GraphicsComplex[Flatten[N[points], 1], {EdgeForm[],
       GraphicsGroup[{Polygon[Flatten[#, 1] &@

           Table[{i lInner + j,
             i lInner + j + 1, (i + 1) lInner + j +
              1, (i + 1) lInner + j}, {i, 0, lOuter - 2}, {j,
             lInner - 1}]]}]},
      VertexNormals -> Flatten[N[normals], 1],
      VertexColors -> Flatten[N[normals], 1]]
     ];
   spherePoints[n_] := spherePoints[n] =
     Module[{[Psi]s = 2. Pi (Range[0, 2 n]/(2 n)), [Phi]s =
        1. Pi (Range[0, n]/n)},
      c[Psi]s = Cos[[Psi]s]; s[Psi]s = Sin[[Psi]s];
      c[Phi]s = Cos[[Phi]s]; s[Phi]s = Sin[[Phi]s];
      [Psi]ones = Table[1., {k, 0, 2 n}];
      xs = Outer[Times, c[Psi]s, s[Phi]s];
      ys = Outer[Times, s[Psi]s, s[Phi]s];
      zs = Outer[Times, [Psi]ones, c[Phi]s];
      Transpose[{xs, ys, zs}, {3, 1, 2}]
      ];
   colors[n_, {l_, m_}, reim_] := colors[n, {l, m}, reim] =
     Module[{[Psi]s = 2. Pi Range[0, 2 n]/(2 n), [Phi]s =
        1. Pi Range[0, n]/n, [Psi]L, [Phi]L,
       hueData, [CapitalDelta]h},
      [Psi]L = reim[Exp[I m [Psi]s]];
      [Phi]L = LegendreP[l, m, Cos[[Phi]s]];
      hueData = Outer[Times, [Psi]L, [Phi]L];
      [CapitalDelta]h =
       If[Max[hueData] == Min[hueData], 1,
        Max[hueData] - Min[hueData]];
      Map[Hue, 0.8 (hueData - Min[hueData])/[CapitalDelta]h, {2}]
      ];
   coloredSphere[l_, m_, reim_, pp_] :=
    Graphics3D[
     makeColoredSphereGraphicsComplex[spherePoints[pp],
      spherePoints[pp], colors[pp, {l, m}, reim]], Boxed -> False,
     ImageSize -> {400, 350}, SphericalRegion -> True,
     ViewAngle -> [Pi]/10];}]