Let $R$ be an Eichler order of an indefinite quaternion algebra $B/\mathbb{Q}$ (suppose B is not the collection of $2\times 2$ matrices) and $S$ the corresponding Shimura Curve. Modular forms of weight $2k$ on $S$ can be written as either

(1) Functions on the idele group $B^*_\mathbb{A}$ of $B$

(2) Holomorphic functions on the upper half plane that satisfy the required transformation property under the corresponding Fuchsian group.

It is well-known that these definitions are equivalent, but I can't find a reference that writes down both

(A) An isomorphism between (1) and (2) in this setting. (which I imagine is just given via pullback under $B^*_\mathbb{A} \xrightarrow{g \mapsto g_\infty(i)} \mathcal{H}$)

(B) Defines the Hecke operators.

Can you please give me a reference? An electronic reference, if available, would be very much appreciated.