A First Course in Modular Forms
《A First Course in Modular Forms》 · 第 195 页 · Section 5.8「Eigenforms」，Definition 5.8.1
The eigenform $f(\tau)=\sum_{n=0}^{\infty}a_n(f)q^n$ is normalized when $a_1(f)=1$. A newform is a normalized eigenform in $S_k(\Gamma_1(N))^{\mathrm{new}}$.