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Questions tagged [modular-forms]

Questions about modular forms and related areas

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Algebraic independece of modular forms for Fricke group over $\mathbb C(q)$

Let $q=e^{\pi i \tau}$ for $\tau \in \mathbb H$ and $$P_2(q)=\frac{P(q)+2P(q^2)}{3}, \quad Q_2(q)=\frac{Q(q)+4Q(q^2)}{5}, \\ R_2(q)=\frac{R(q)+8R(q^2)}{9},$$ a Fourier series of quasi-modular form ...
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About different cohomology theories used to study Shimura varieties

The classical theory of Eichler-Shimura realizes the space of cusp forms of certain weights and levels in the parabolic cohomology of modular curves, which is the image of the cohomology with compact ...
120 views

Characterizing a modular form via its first Fourier coefficients at infinity

It is well known that a cusp form $$f = \sum_{n\ge 1}a_n q^n$$ of weight $k$ and level $1$ is determined by its first $d_k = \text{dim } S_k$ coefficients. This follows from the valence formula (...
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Terminology question for the cohomology of the Hilbert modular group

Let $\Gamma$ be the Hilbert modular group of determinant one matrices with entries in the ring of integers of a real quadratic field $F$, and let $M$ be a $\Gamma$-module. Is there a standard name for ...

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