2 problems

Let $f=\sum_n a_nq^n$ be a newform of weight $1$ and level $\Gamma_1(N)$. Let $\rho_f$ be its Deligne–Serre representation, let ${\mathrm{Ad}}(\rho_f)$ be the trace-free adjoint re…

Let $f$ be a newform of weight $1$ and level $N$, with associated representation $\rho_f$. Let $\mathcal{U}(\operatorname{Ad}(\rho_f))$ be the equivariant unit module, and let…