This paper investigates the relation between Toda brackets and congruences of modular forms. It determines the –invariant of Toda brackets and thereby generalizes the formulas of J F Adams for the classical –invariant to the chromatic second filtration.
"Toda brackets and congruences of modular forms." Algebr. Geom. Topol. 11 (4) 1893 - 1914, 2011. https://doi.org/10.2140/agt.2011.11.1893