  We prove an unconditional power saving for the dimension of the space of
cohomological automorphic forms of fixed level and growing weight on GL_2 over
any number field which is not totally real. Our proof involves the theory of
p-adically completed cohomology developed by Calegari and Emerton, and a bound
for the growth of coinvariants in certain finitely generated non-commutative
Iwasawa modules.
