  Feynman integrals are central to all calculations in perturbative Quantum
Field Theory. They often give rise to iterated integrals of dlog-forms with
algebraic arguments, which in many cases can be evaluated in terms of multiple
polylogarithms. This has led to certain folklore beliefs in the community
stating that all such integrals evaluate to polylogarithms. Here we discuss a
concrete example of a double iterated integral of two dlog-forms that evaluates
to a period of a cusp form. The motivic versions of these integrals are shown
to be algebraically independent from all multiple polylogarithms evaluated at
algebraic arguments. From a mathematical perspective, we study a mixed elliptic
Hodge structure arising from a simple geometric configuration in
$\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lines
which meet it at torsion points, which may provide an interesting worked
example from the point of view of periods, extensions of motives, and
L-functions.
