Ramanujan's Eisenstein series and powers of Dedekind's eta-function

In this article, we use the theory of elliptic functions toconstruct theta function identities which are equivalent toMacdonald's identities for A₂, B₂ and G₂. Using these identities,we express, for d = 8, 10 or 14, certain theta functions inthe form ^d()F(P, Q, R), where () is Dedekind's eta-function,and F(P, Q, R) is a polynomial in Ramanujan's Eisenstein seriesP, Q and R. We also derive identities in the case when d = 26.These lead to a new expression for ²⁶(). This work generalizesthe results for d = 1 and d = 3 which were given by Ramanujanon page 369 of ‘The Lost Notebook’.