  
  
                            [1XThe [5XModularGroup[105X Package[101X
  
  
                      [1XFinite-index subgroups of [22X(P)SL_2(ℤ)[122X[101X
  
  
                                 Version 2.0.3
  
  
                                  17 June 2026
  
  
                              Sebastian Engelhardt
  
                                  Luca L. Junk
  
                                 Hannah Wagmann
  
                          Gabriela Weitze-Schmithüsen
  
  
  
  Sebastian Engelhardt
      Email:    [7Xmailto:seen00001@stud.uni-saarland.de[107X
      Homepage: [7Xhttps://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen.html[107X
  Luca L. Junk
      Email:    [7Xmailto:junk@math.uni-sb.de[107X
      Homepage: [7Xhttps://www.uni-saarland.de/lehrstuhl/weber-moritz/team/luca-junk.html[107X
  Hannah Wagmann
      Email:    [7Xmailto:wagmann@math.uni-sb.de[107X
      Homepage: [7Xhttps://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen/team/hannah-wagmann.html[107X
  Gabriela Weitze-Schmithüsen
      Email:    [7Xmailto:weitze@math.uni-sb.de[107X
      Homepage: [7Xhttps://www.uni-saarland.de/lehrstuhl/weitze-schmithuesen/team/gabriela-weitze-schmithuesen.html[107X
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y©  2026  by  Sebastian Engelhardt, Luca L. Junk, Hannah Wagmann and Gabriela
  Weitze-Schmithüsen[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YSupported  by  Project I.8 of SFB-TRR 195 'Symbolic Tools in Mathematics and
  their Application' of the German Research Foundation (DFG).[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (ModularGroup)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YGeneral aims of the [5XModularGroup[105X package[133X
    1.2 [33X[0;0YTechnicalities[133X
  2 [33X[0;0YSubgroups of [22XSL_2(ℤ)[122X[133X
    2.1 [33X[0;0YConstruction of modular subgroups[133X
      2.1-1 [33X[0;0YModularSubgroup[133X
      2.1-2 [33X[0;0YModularSubgroupST[133X
      2.1-3 [33X[0;0YModularSubgroupRT[133X
      2.1-4 [33X[0;0YModularSubgroupSJ[133X
      2.1-5 ModularSubgroup
    2.2 [33X[0;0YGetters for the coset action[133X
      2.2-1 [33X[0;0YSAction[133X
      2.2-2 [33X[0;0YTAction[133X
      2.2-3 [33X[0;0YRAction[133X
      2.2-4 [33X[0;0YJAction[133X
      2.2-5 [33X[0;0YCosetActionOf[133X
    2.3 [33X[0;0YComputing with modular subgroups[133X
      2.3-1 Index
      2.3-2 GeneralizedLevel
      2.3-3 [33X[0;0YCosetRepresentatives[133X
      2.3-4 WordGeneratorsOfGroup
      2.3-5 GeneratorsOfGroup
      2.3-6 IsCongruence
      2.3-7 Cusps
      2.3-8 CuspWidth
      2.3-9 CuspsEquivalent
      2.3-10 CosetRepresentativeOfCusp
      2.3-11 IndexModN
      2.3-12 Deficiency
      2.3-13 Deficiency
      2.3-14 Projectivization
      2.3-15 ConjugateGroup
      2.3-16 NormalCore
      2.3-17 QuotientByNormalCore
      2.3-18 AssociatedCharacterTable
      2.3-19 IsElementOf
      2.3-20 IsWordElementOf
      2.3-21 IsWordElementOf
      2.3-22 Genus
    2.4 [33X[0;0YMiscellaneous[133X
      2.4-1 DefinesCosetActionST
      2.4-2 DefinesCosetActionRT
      2.4-3 DefinesCosetActionSJ
      2.4-4 [33X[0;0YCosetActionFromGenerators[133X
      2.4-5 STDecomposition
      2.4-6 RTDecomposition
      2.4-7 SJDecomposition
      2.4-8 STDecompositionAsList
  3 [33X[0;0YSubgroups of [22XPSL_2(ℤ)[122X[133X
    3.1 [33X[0;0YConstruction of projective modular subgroups[133X
      3.1-1 [33X[0;0YProjectiveModularSubgroup[133X
    3.2 [33X[0;0YGetters for the coset action[133X
      3.2-1 [33X[0;0YSAction[133X
      3.2-2 [33X[0;0YTAction[133X
    3.3 [33X[0;0YComputing with projective modular subgroups[133X
      3.3-1 Index
      3.3-2 GeneralizedLevel
      3.3-3 [33X[0;0YCosetRepresentatives[133X
      3.3-4 GeneratorsOfGroup
      3.3-5 IsCongruence
      3.3-6 Cusps
      3.3-7 CuspWidth
      3.3-8 CuspsEquivalent
      3.3-9 CosetRepresentativeOfCusp
      3.3-10 LiftToSL2ZEven
      3.3-11 LiftToSL2ZOdd
      3.3-12 IndexModN
      3.3-13 Deficiency
      3.3-14 Deficiency
      3.3-15 ConjugateGroup
      3.3-16 NormalCore
      3.3-17 QuotientByNormalCore
      3.3-18 AssociatedCharacterTable
      3.3-19 IsMatrixElementOf
      3.3-20 IsWordElementOf
      3.3-21 IsElementOf
      3.3-22 Genus
  
  
  [32X
