L-function of a modular form

《A First Course in Modular Forms》 · 第 200 页 · Section 5.9「The connection with L-functions」

Each modular form $f\in M_k(\Gamma_1(N))$ has an associated Dirichlet series, its L-function. Let $f(\tau)=\sum_{n=0}^{\infty}a_nq^n$ and write formally $L(s,f)=\sum_{n=1}^{\infty}a_nn^{-s}$.