Did Hermite solve the quintic equation by canceling weights to form an invariant variable via modular transformations?

I am trying to understand the deep mechanism behind Charles Hermite's solution to the general quintic equation using elliptic modular functions.

As I understand it, under the 12 modular transformations of order 5 (associated with the modular equation of degree 6), the relevant modular forms transform with a specific "weight." However, by properly combining these forms, Hermite managed to cancel out the weight factors. This allowed him to construct a variable (an invariant or modular function) whose value does not change in form, ultimately leading to the roots of the quintic equation.Is this intuition correct? Specifically, is it accurate to say that the core of Hermite's method relies on canceling the weights under the 12 modular transformations to produce weight-0 modular functions (invariants), which then correspond to the algebraic symmetries of the quintic?

Any insights, historical context, or technical clarifications would be greatly appreciated.