In "On $\ell$-adic representations attached to modular forms II", Ribet proved that the $\ell$-adic representation $\rho_{f,\ell}$ attached to a non-CM newform form $f$ satisfies $${\rm SL}_2(\mathbb{F}_\ell)\subset \overline{\rho}_{f,\ell}(G_\mathbb{Q}).\qquad\qquad(*)$$ I am wondring :

(i)- Why $(*)$ implies that $\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is absolutely irreducible?

(ii)- Let $n$ be a positive integer. Dose $(*)$ implies that ${\rm Sym}^n\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is irreducible? If the answer is negative, under what condition does this hold?

In "On $\ell$-adic representations attached to modular forms II", Ribet proved that the $\ell$-adic representation $\rho_{f,\ell}$ attached to a non-CM newform form $f$ satisfies $${\rm SL}_2(\mathbb{F}_\ell)\subset \overline{\rho}_{f,\ell}(G_\mathbb{Q}).\qquad\qquad(*)$$

I am wondering:

(i) Why does $(*)$ imply that $\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is absolutely irreducible?

(ii) Let $n$ be a positive integer. Does $(*)$ imply that ${\rm Sym}^n\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is irreducible? If the answer is negative, under what condition does this hold?

In "On $\ell$-adic representations attached to modular forms II", Ribet proved that the $\ell$-adic representation $\rho_{f,\ell}$ attached to a non-CM newform form $f$ satisfies $${\rm SL}_2(\mathbb{F}_\ell)\subset \overline{\rho}_{f,\ell}(G_\mathbb{Q}).\qquad\qquad(*)$$ I am wondring :

(i)- Why $(*)$ implies that $\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is absolutely irreducible?

(ii)- Let $n$ be a positive integer. Dose $(*)$ implies that ${\rm Sym}^n\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is absolutly irreducible? If the answer is negative, under what condition does this hold?

In "On $\ell$-adic representations attached to modular forms II", Ribet proved that the $\ell$-adic representation $\rho_{f,\ell}$ attached to a non-CM newform form $f$ satisfies $${\rm SL}_2(\mathbb{F}_\ell)\subset \overline{\rho}_{f,\ell}(G_\mathbb{Q}).\qquad\qquad(*)$$ I am wondring :

(i)- Why $(*)$ implies that $\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is absolutely irreducible?

(ii)- Let $n$ be a positive integer. Dose $(*)$ implies that ${\rm Sym}^n\overline{\rho}_{f,\ell|G_{\mathbb{Q}(\zeta_\ell)}}$ is irreducible? If the answer is negative, under what condition does this hold?