Let 
be a positive integer, then 
is defined as the set of all matrices ![[a b; c d]](/images/equations/ModularGroupGamma0/Inline3.svg)
in the modular
group Gamma 
with 
.
is a subgroup of 
. For any prime 
, the set
 |
is a fundamental region of the subgroup 
, where 
and 
(Apostol 1997).
Modular Group Gamma_0
See also
Modular Group Gamma, Modular Group Lambda, Supersingular PrimeExplore with Wolfram|Alpha
References
Apostol, T. M. "The Subgroup
" and "Fundamental Region 
." §4.2-4.3 in Modular
Functions and Dirichlet Series in Number Theory, 2nd ed. New York: Springer-Verlag,
pp. 75-78, 1997.
Cite this as:
Weisstein, Eric W. "Modular Group Gamma_0." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ModularGroupGamma0.html