  We construct elements in the group $K_4$ of modular curves using the
polylogarithmic complexes of weight 3 defined by Goncharov and De Jeu. The
construction is uniform in the level and uses new modular units obtained as
cross-ratios of division values of the Weierstrass $\wp$ function. These units
provide explicit triangulations of the $3$-term relations in $K_2$ of modular
curves, which in turn give rise to elements in $K_4$. Based on numerical
computations and on recent results of W. Wang, we conjecture that these
elements are proportional to the Beilinson elements defined using the
Eisenstein symbol.
