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The ModularGroup Package

Finite-index subgroups of (P)SL_2(ℤ)

Version 2.0.0

14 July 2022

Luca L. Junk
Email: junk@math.uni-sb.de
Homepage: https://www.uni-saarland.de/lehrstuhl/weber-moritz/team/luca-junk.html
Address:
Saarland University
Department of Mathematics
Postfach 15 11 50
66041 Saarbrücken
Germany

Gabriela Weitze-Schmithüsen
Email: weitze@math.uni-sb.de
Homepage: http://www.math.uni-sb.de/ag/weitze/
Address:
AG Weitze-Schmithüsen
FR 6.1 Mathematik
Universität des Saarlandes
D-66041 Saarbrücken

Copyright

© 2022 by Luca L. Junk and Gabriela Weitze-Schmithüsen

Acknowledgements

Supported by Project I.8 of SFB-TRR 195 'Symbolic Tools in Mathematics and their Application' of the German Research Foundation (DFG).

Contents

1 Introduction
 1.1 General aims of the ModularGroup package
 1.2 Technicalities
2 Subgroups of SL_2(ℤ)
 2.1 Construction of modular subgroups

  2.1-1 Constructors
  2.1-2 Getters for the coset action
 2.2 Computing with modular subgroups

  2.2-1 Index
  2.2-2 GeneralizedLevel
  2.2-3 RightCosetRepresentatives
  2.2-4 GeneratorsOfGroup
  2.2-5 MatrixGeneratorsOfGroup
  2.2-6 IsCongruence
  2.2-7 Cusps
  2.2-8 CuspWidth
  2.2-9 CuspsEquivalent
  2.2-10 CosetRepresentativeOfCusp
  2.2-11 IndexModN
  2.2-12 Deficiency
  2.2-13 Deficiency
  2.2-14 Projection
  2.2-15 Conjugate
  2.2-16 NormalCore
  2.2-17 QuotientByNormalCore
  2.2-18 AssociatedCharacterTable
  2.2-19 IsElementOf
  2.2-20 Genus
 2.3 Miscellaneous

  2.3-1 DefinesCosetActionST
  2.3-2 DefinesCosetActionRT
  2.3-3 DefinesCosetActionSJ
  2.3-4 CosetActionFromGenerators
  2.3-5 STDecomposition
  2.3-6 RTDecomposition
  2.3-7 SJDecomposition
  2.3-8 STDecompositionAsList
3 Subgroups of PSL_2(ℤ)
 3.1 Construction of projective modular subgroups

  3.1-1 Constructors
  3.1-2 Getters for the coset action
 3.2 Computing with projective modular subgroups

  3.2-1 Index
  3.2-2 GeneralizedLevel
  3.2-3 RightCosetRepresentatives
  3.2-4 GeneratorsOfGroup
  3.2-5 IsCongruence
  3.2-6 Cusps
  3.2-7 CuspWidth
  3.2-8 CuspsEquivalent
  3.2-9 CosetRepresentativeOfCusp
  3.2-10 LiftToSL2ZEven
  3.2-11 LiftToSL2ZOdd
  3.2-12 IndexModN
  3.2-13 Deficiency
  3.2-14 Deficiency
  3.2-15 Conjugate
  3.2-16 NormalCore
  3.2-17 QuotientByNormalCore
  3.2-18 AssociatedCharacterTable
  3.2-19 IsElementOf
  3.2-20 Genus
References
Index

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