Ihara's lemma for Shimura curves with arbitrary weight

Let $F$ be a totally real field, let $D$ be a quaternion algebra over $F$ ramified at exactly one infinite place, and let $\mathfrak{p}$ be a finite place at which $D$ is unramified. Let $K\subseteq G(\mathbb{A}_{F,f})$ be sufficiently small and unramified at $\mathfrak{p}$, let $S$ contain $\Sigma(K)\cup\Sigma_l\cup\{\mathfrak{p}\}\cup\Sigma_\infty$, and let $\pi_1,\pi_2:X_{K_0(\mathfrak{p})}\to X_K$ be the degeneracy maps. Let $\Lambda$ be the local system on $X_K$ attached to a finite-dimensional continuous $\mathbb{F}_l$-representation of $K^{\mathfrak{p}}$. Ihara's lemma for arbitrary weight. For every non-Eisenstein maximal ideal $\mathfrak{m}$ of $\mathbb{T}^S_{\mathbb{Z}_l}$, the map

$$\pi_1^*\oplus\pi_2^*:H^1_{\mathrm{\acute{e}t}}(X_K,\Lambda)_\mathfrak{m}\oplus H^1_{\mathrm{\acute{e}t}}(X_K,\Lambda)_\mathfrak{m}\longrightarrow H^1_{\mathrm{\acute{e}t}}(X_{K_0(\mathfrak{p})},\Lambda)_\mathfrak{m}$$

is injective. This is the expected Ihara lemma for Shimura curves with coefficients in arbitrary algebraic local systems; the constant-sheaf case is the weight-two specialization, and the statement remains conjectural in the generality considered here.