(Sorry for my poor english..)
Let $\ell$ be a prime and $\mathbb{F}_{\ell}$ be a finite field with $\ell$ elements. Let $\chi_{\ell}$ be a mod $\ell$-adic cyclotomic character, i.e. \begin{equation} \chi_{\ell} : Gal(\overline{\mathbb{Q}}/\mathbb{Q})\to \mathbb{F}_{\ell}^{*}. \end{equation} Consider a two-dimensional Galois representation $\rho$ such that \begin{equation} \rho : Gal(\overline{\mathbb{Q}}/\mathbb{Q})\to GL_2(\mathbb{F}_{\ell}) \end{equation} with unramified at $\ell$ and $$ \rho =\begin{bmatrix} \chi_{\ell} & *\\ 0 & 1 \end{bmatrix}.$$ How many $\rho$ are there? (It means that how many $*$ satisfying above condition?)