Non-Eisenstein Ihara conjecture for Shimura curves

Let $q$ be a prime number such that $q\not|N\Delta\ell$. Fix a maximal non-Eisenstein ideal $\mathfrak m$ of the Hecke algebra ${\bf T}^{\widehat\psi}(N)$ acting on $H^1({\bf X}_1(N),\mathcal O)^{\widehat\psi}$. Let ${\bf T}^{\widehat\psi}(N,q)$ be the Hecke algebra acting on $H^1({\bf X}_1(N,q),\mathcal O)^{\widehat\psi}$, and let $\mathfrak m_q$ be the inverse image of $\mathfrak m$ under the natural map ${\bf T}^{\widehat\psi}(N,q)\to {\bf T}^{\widehat\psi}(N)$. Non-Eisenstein Ihara conjecture. The map

$$\alpha_{\mathfrak m}:H^1({\bf X}_1(N),\mathcal O)_{\mathfrak m}^{\widehat\psi}\times H^1({\bf X}_1(N),\mathcal O)_{\mathfrak m}^{\widehat\psi}\to H^1({\bf X}_1(N,q),\mathcal O)_{\mathfrak m_q}^{\widehat\psi}$$

has a torsion-free cokernel. This is a non-Eisenstein version of the problem of Ihara for degeneracy maps between Shimura curves; the source describes the corresponding torsion-freeness assertion as an open problem.