  We present a deterministic algorithm for computing spaces of weight 1 modular
forms with exotic representations. This algorithm is an improved version of
Schaeffer's Hecke stability method, utilising the author's previous work on the
twist-minimal trace formula for weight 2 holomorphic forms, and presenting a
method of lifting forms from characteristic p. The algorithm was used to
compute all such forms with level at most 10,000. Together with Sutherland's
computation of dihedral forms, this allows us to present the dimensions of all
weight 1 newform spaces up to level 10,000.
