# Questions tagged [modular-forms]

Questions about modular forms and related areas

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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 $\ell$-...
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### Maximum value of newform from Galois representation

One can attach $\ell$-adic Galois representations to holomorphic cuspidal newforms of weight $2$ on the upper half-plane. If a newform is $L^2$-normalized, can one extract its maximum value from the ...
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### Meaning of Atkin-Lehner eigenvalues

Suppose I have $f\in S_2(\Gamma_0(N))$ a classical modular newform of level $N$. I want to understand what information (if any) is carried by its Atkin-Lehner eigenvalues for primes $p\mid N$, as ...
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### Modular forms on $\Gamma(N)$

I'm wondering where I can find a good reference about what is known about modular forms (especially cuspidal eigenforms) of full principal level $\Gamma(N)$, in terms of their Hecke theory, old/...
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### Hurwitz numbers and $t$-cores

For integers $k \geq 0$ and $d \geq 1$ let $H(k,d)$ be the Hurwitz number which, for the purposes of this posting, will be defined by: H(k,d) \, := \ d! \, \sum_{\lambda \, \vdash d}...
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### Modular form not meromorphic at $\infty$

Is there a function $f$ with the following properties $f$ meromorphic at the upper half plane $\mathfrak h$, $f$ is of weight $k$ under a congruence subgroup of $\operatorname{SL}_2(\mathbb Z)$, $f$ ...
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### Is there some precise way in which modular cocycle $c/(c\tau +d)$ “is” the generator of $H^1(\mathcal{M}_{ell}, \omega^2) \cong \mathbb{Z}/12$?

It is semiclassical that the extension class $\text{Ext}^1(\omega^{-1},\omega)\cong H^1(\mathcal{M}_{ell},\omega^2)$ over the modular stack $\mathcal{M}_{ell}/\mathbb{Z}$ is nonvanishing, being cyclic ...
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### Reference request for some fragments of Gauss with dubious origin

Gauss's results on the interconnection between the different values of the arithmetic-geometric mean of two complex numbers as recorded in his private notebooks led him to introduce foundational ...
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