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Feynman integrals are central to all calculations in perturbative QuantumField Theory. They often give rise to iterated integrals of dlog-forms withalgebraic arguments, which in many cases can be evaluated in terms of multiplepolylogarithms. This has led to certain folklore beliefs in the communitystating that all such integrals evaluate to polylogarithms. Here we discuss aconcrete example of a double iterated integral of two dlog-forms that evaluatesto a period of a cusp form. The motivic versions of these integrals are shownto be algebraically independent from all multiple polylogarithms evaluated atalgebraic arguments. From a mathematical perspective, we study a mixed ellipticHodge structure arising from a simple geometric configuration in$\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lineswhich meet it at torsion points, which may provide an interesting workedexample from the point of view of periods, extensions of motives, andL-functions.

A double integral of dlog forms which is not polylogarithmic