  In these proceedings we discuss a representation for modular forms that is
more suitable for their application to the calculation of Feynman integrals in
the context of iterated integrals and the differential equation method. In
particular, we show that for every modular form we can find a representation in
terms of powers of complete elliptic integrals of the first kind multiplied by
algebraic functions. We illustrate this result on several examples. In
particular, we show how to explicitly rewrite elliptic multiple zeta values as
iterated integrals over powers of complete elliptic integrals and rational
functions, and we discuss how to use our results in the context of the system
of differential equations satisfied by the sunrise and kite integrals.
