  Let $k:=\mathbb{F}_q$ be the finite field of $q$ elements and $E$ an elliptic
curve over $k$ given by the equation $f(x,y) = 0$. Let $k[E]$ the affine
coordinate ring and $k(E)$ the field of fractions. We fix a place $\infty$ of
$k(E)$ and let $k_{\infty}$ be the completion. The group ${\rm{GL}}_2(k[E])$
acts on the symmetric space $\mathcal{T}$, the Bruhat-Tits building of
${\rm{PGL}}_2(k_{\infty})$. In this paper, we use the quotient space to
construct the space of modular symbols over $K(E)$. We prove that this space is
given by an explicit set of generators and their relations.
