  We study modular determinantal differential equations of orders 2 and 3. We
show that the expansion of the analytic solution of a non-degenerate modular
equation of type D3 over the rational numbers with respect to the natural
parameter coincides, under certain assumptions, with the q-expansion of the
newform of its spectral elliptic curve and therefore possesses a
multiplicativity property. We compute the complete list of D3 equations with
this multiplicativity property and relate it to Zagier's list of non-degenerate
modular D2 equations.
