Let $C_5:=\{{(z_1 \dots, z_5) \in (\mathbb{C})^5 | z_i \neq z_j \forall i\neq j }\}$ be the configuration space of five distinct ordered points in $\mathbb{C}$. Arnold showed that the holomorphic one forms $w_{i,j}:=d log (z_i - z_j)$ satisfy the relation 
$w_{i,j}\wedge w_{j,k}\wedge w_{k,l}=0$.

Let $\mathcal{A}_2[2]$ be the space of principally polarized abelian surfaces with level 2 structure. Since $C_5$ parametrizes genus 2 curves with an ordering on their Weirstrass points the Torelli map gives an injection 
$T:C_5/G \hookrightarrow \mathcal{A}_2[2]$ 
whose image is the complement of the divisor parametrizing Abelian surfaces which are products of two elliptic curves. Here $G$ is the 2-dimensional group of affine transformations of $\mathbb{C}$.  

Is it known which theta functions (perhaps with characteristics) on $\mathcal{A}_2[2]$ pull back to differential forms $w_{i,j}=dlog(z_i -z_j)$ on $C_5$ by the Torelli map $T$? Is the analog of Arnold's relation for $w_{i,j}$ known for such theta functions? 

Any comments or references are more than welcome.