Suppose that $f \in S_k(\Gamma_0(N)) $ be a Hecke eigenform whose Fourier expansion at $ i\infty $ is given by
$$ f(z) = \sum_{n=1}^{\infty} \lambda(n) n^{\frac{k-1}{2}} \exp(2\pi i n z), $$
normalized so that $\lambda(1)=1$. In this setting the Ramanujan-Petersson conjecture states that $ |\lambda(n)| \leq d(n) $ the number of divisors of $n$ (for all $ n $ coprime to the level $ N $).
Does the same bound hold if I consider the Fourier expansion of $f$ at some other cusp?