The paper here posits on page 86 that it is Shimura who proved in "Introduction to the Arithmetic Theory of Automorphic Functions" that for a prime $p$, the $p$-adic Galois representation attached to a newform $f = \sum_{n = 1}^\infty a_n q^n$ of weight $2$, level $N_f$ and character $\epsilon$
$$\rho_f: G_{\mathbb Q} \to \operatorname{GL}_2(\mathcal O_f)$$
satisfies $\operatorname{trace}(\rho_f(\operatorname{Frob}_l)) = a_l$ and $\det(\rho_f(\operatorname{Frob}_l)) = \epsilon(l)l$ for all primes $l \nmid Np$. However, I cannot seems to locate anywhere in the text a result that looks anything like this. Where can I find this result without having to resign myself to Deligne's general recipe?