A First Course in Modular Forms
《A First Course in Modular Forms》 · 第 195 页 · Section 5.8「Eigenforms」，Definition 5.8.1
A nonzero modular form $f\in M_k(\Gamma_1(N))$ that is an eigenform for the Hecke operators $T_n$ and $\langle n\rangle$ for all $n\in\mathbb Z^+$ is a Hecke eigenform or simply an eigenform.