At the beginning of Haruzo Hida's article "Big Galois representations and $p$-adic L functions", he has defined $$\chi_1= \textrm{the } N_0 \textrm{-part of} \chi \times \textrm{the tame } p\textrm{-part of} \chi.$$ Here $N_0$ is an integer prime to $p$ and $\chi$ is a Dirichlet character modulo $N_0p^r$.
So does that mean $\chi_1=\chi\vert_{(\mathbb{Z}/N_0)^\ast\times\mathbb{Z}/(p-1)\mathbb{Z}}$?