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 $R$ be the ring of integers of $L$, with $6N$ inverted, and let $g$ be the weight-one form with associated representation $\rho_g$. Define … Let $\mathfrak{S}$ be the Shimura c…