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I am familiar with the theory of Hida families of modular forms, so Hida theory on $GL_2$, but I am not familiar with Hida theory on any other algebraic groups. My question concerns Hida families of ...

Let $a(n)$ and $b(n)$ be define by the following; $E_6/E_4 = 1 - 744q + 159768q^2 - 36866976q^3 + 8507424792q^4 - 1963211493744q^5 + \cdots = \Sigma a(n)q^n,$ $E_8/E_6 = 1 + 984q + 574488q^2 + ...