  Let $\text{Emb}_{\mathbb{Z}}^+(\mathrm{O})$ denote $\mathbb{Z}-$linear formal
sums of equivalence classes of optimal embeddings of real quadratic orders into
$\mathrm{O}$, an Eichler order of level $\mathfrak{M}$ in an indefinite
quaternion algebra over $\mathbb{Q}$. For all positive integers $n$ coprime to
$\mathfrak{M}$, we define an operator
$T_n:\text{Emb}_{\mathbb{Z}}^+(\mathrm{O})\rightarrow
\text{Emb}_{\mathbb{Z}}^+(\mathrm{O})$, which we refer to as a Hecke operator.
We introduce the "prime power Hecke graph", and show how it can be used to
determine the effect of $T_p$ on a single optimal embedding. To justify the
name of the operator, we associate an optimal embedding equivalence class to a
closed geodesic on the corresponding Shimura curve. By considering the signed
intersection number of pairs of geodesics, we use the operators $T_n$ to define
formal power series. In showing that the action of Hecke operators on the
homology of the curve commutes with our definition, we prove that the formal
power series agree with weight two cusp forms for $\Gamma_0(N)$ on all
coefficients of exponents coprime to $\mathfrak{M}$.
