Nội dung: This talk aims at introducing Hecke operators on the space $M_k(Gamma_1(N))$. The subspace $S_k(Gamma_1(N))$ can then be made into an inner product space, on which the Hecke operators away from $N$ act as commuting normal operators. It then follows by linear algebra that $S_k(Gamma_1(N))$ has an orthogonal basis consisting of simultaneous eigenvectors for these operators. We will also see that these basis elements when suitably normalized, give rise to Dirichlet series which admit an Euler product expansion.