The (higher order) Johnson homomorphism embeds the associated graded Lie algebra for the mapping class group of a once punctured surface into a certain Lie algebra. Calculating the image of the Johnson homomorphism is a challenging problem. Shigeyuki Morita was the first to define obstructions to lying in the image back in the 90s. More recently Enomoto and Satoh have defined a new series of obstructions, and work of Conant-Kassabov-Vogtmann has provided a rich family of obstructions, involving classical modular forms, stemming from the abelianization of the target Lie algebra. In this talk, I will present joint work with Martin Kassabov which simultaneously generalizes all of these obstructions, making use of an apparently new action of $Aut(F_n) on H^{\otimes n}$ for any cocommutative Hopf algebra H.