# Questions tagged [modular-forms]

A modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group.

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### A simple question in the proof that Hecke operators commute

So I am reading these lecture notes by Don Zagier and in his proof of theorem 2.1 he first shows that the Fourier expansion of T_n f is given by \begin{align*} T_{n}f(z)=\sum_{m=0}^{\infty}\sum_{r|n,m}...
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### Base change of $H^n(\Gamma, \mathrm{Sym}^{k}(R^2))$ - A small step in Eichler-Shimura

I'm currently learning Eichler-Shimura mapping and found the note by Gabor Wiese is quite helpful. Yet I have come up with a quite detailed question. Let $R$ be a ring (all rings in this post are ...
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### On Fourier coefficients of Bianchi modular forms, l-ordinary

Let $f\in S_2(\Gamma_1(N))$ be a Hecke eigenform and $\ell$ a prime number does not divide $N$. Let $a_f(\ell)$ be the $\ell$-th Fourier coefficient of $f$. Then $a_f(\ell)$ is is called $\ell$-...