The set 
of linear Möbius transformations w which satisfy
where a and d are odd and b and c are even. is a subgroup of the modular group gamma, and is also called the theta subgroup. The fundamental region of the modular lambda group is illustrated above.
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 113-114, 1987.