  We present two approaches that can be used to compute modular forms on
noncongruence subgroups. The first approach uses Hejhal's method for which we
improve the arbitrary precision solving techniques so that the algorithm
becomes about up to two orders of magnitude faster in practical computations.
This allows us to obtain high precision numerical estimates of the Fourier
coefficients from which the algebraic expressions can be identified using the
LLL algorithm. The second approach is restricted to genus zero subgroups and
uses efficient methods to compute the Belyi map from which the modular forms
can be constructed.
