I found the group in a newspaper $ Gamma_0 (18) $ can be generated by the following list of matrices:

$ displaystyle left ( begin {array} {rr} 7 & 1 \ 36 & 5 end {array} right) $

$ displaystyle left ( begin {array} {rr} 13 & 8 \ 18 & 11 end {array} right) $

$ displaystyle left ( begin {array} {rr} 71 & 15 \ 90 & 9 end {array} right) $
 $ displaystyle left ( begin {array} {rr} 55 & 13 \ 72 & 17 end {array} right) $
 $ displaystyle left ( begin {array} {rr} 7 & 2 \ 18 & 5 end {array} right) $
 $ displaystyle left ( begin {array} {rr} 31 & 25 \ 36 & 29 end {array} right) $
 $ displaystyle left ( begin {array} {rr} 1 & 1 \ 0 & 1 end {array} right) $
 $ displaystyle left ( begin {array} {rr} 1 & 0 \ 0 & 1 end {array} right) $
E.g. $ 31 times (29) – 36 times (25) = 899 + 900 = $ 1 Actually, $ 36, 18, 19 equiv 0 pmod {18} $.
These generators look anything. There is a list of generators from $ Gamma_0 (N) $ to the $ N <100 $ ?
Is there a computer program or algorithm for finding generators of congruence groups, for example using a linear algebra package such as e.g. sage
?