Hecke structure of quaternionic modular forms mod $p$

We relate the systems of Hecke eigenvalues arising from the (mod $p$) modular forms on the Shimura curve attached to the indefinite quaternion algebra $B$ of discriminant $δ$ over $\mathbf{Q}$ to the systems of Hecke eigenvalues arising from the (mod $p$) algebraic modular forms attached to the defi