3 problems

Let $f$ be a $p$-new eigenform, let $\mathfrak{p}$ be a prime above $p$, let $V_{\mathfrak{p}}(f)$ be the corresponding $p$-adic representation, let ${\Greekmath 011F}$ be a charac…

Let f\in S_k(\Gamma_0(pN^+))^{p\relax\protect\ifmmode\expandafter\text@\else\expandafter\text\fi{-new}} be a $p$-new eigenform, let $L_{f,\mathfrak{p}}$ be the completion of its…

Let $K$ be the real quadratic field, let $H_{\mathcal{O}}/K$ be the narrow ring class field attached to an order $\mathcal{O}$, let $V_p$ be the relevant $p$-adic representation, a…