  A systematic procedure for generating cubic multisections of Eisenstein
series is given. The relevant series are determined from Fourier expansions for
Eisenstein series by restricting the congruence class of the summation index
modulo three. We prove that the resulting series are rational functions of
\eta(\tau) and \eta(3\tau), where \eta is the Dedekind eta function. A more
general treatment of cubic dissection formulas is given by describing the
dissection operators in terms of linear transformations. These operators
exhibit properties that mirror those of similarly defined quintic operators.
