Power Series Expansion of Dedekind Eta Function: How to Expand η(τ)/η(3τ)?

[twoforone]

Hi Every body!

I wan to compute the power series expansion of dedekind eta function. Specifically, I want to know the power series expansion of η(τ)/η(3τ)? How could I expand this function? I would be happy if you could help me as I am stuck at this state when I am computing the modular polynomial of prime number 3.

 

[camilus]

is eta the alternating zeta function??

 

[twoforone]

eta function is a function with this expression
infinity
η(τ)=q^24 ∏(1-q^n)
n=0
where q=e^2πiτ
Sorry, the product is from n=0 up-to infinity. You should understand in that way.