nt.number theory – How to obtain the ideal used in section 7 of deformation spaces associated with hyperbolic collectors, by Johnson and Millson

I am currently reading the newspaper Deformation spaces associated with hyperbolic collectors by Johnson and Millson, and the bit highlighted below has been giving me difficulties:

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Specifically, how do we define this ideal? $ frak {a} $ That allows us to obtain this group. $ Gamma = Gamma ( frak {a}) $? I tried to follow the reference to Geometrical construction of cohomology for arithmetic groups. by Millson and Raghunathan, but unfortunately, despite my best efforts, I have really struggled to follow this last document and extract something useful, since I am not only new to hyperbolic geometry, but I am not familiar with the theory of numbers either.

If someone could describe specifically how to define that ideal and the group $ Gamma $, I would really appreciate it!