We prove that, for fixed level $$(N,p) = 1$$ and $$p > 2$$ , there are only finitely many Hecke eigenforms f of $$\Gamma _1(N)$$ even weight with $$a_p(f) 0$$ which not CM.

We express the Fourier coefficients of the Hilbert cusp form Lhf associated with mixed Hilbert cusp forms f and h in terms of the Fourier coefficients of a certain periodic function determined by f and h. We also obtain an expression of each Fourier coefficient of Lhf as an infinite series involving the Fourier coefficients of f and h.