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Questions about modular forms and related areas

5 votes
0 answers
228 views

Diophantine applications of Paramodularity

I’ve asked this question to quite a few people in person and so far haven’t seen a good answer... but I believe one should exist, so here goes! Ok, we all know how to (roughly) prove Fermat’s Last The …
4 votes
0 answers
66 views

$3$-variable Jacobi style identity linked to generalised Frobenius partitions

I was fiddling around with a family of probabilistic models and came across two "identities", which appear to be linked to generalized Frobenius partitions (more on this below). I would be grateful if …
9 votes
0 answers
210 views

Surjectivity of reduction for Hilbert modular forms

Fix a totally real field $K$, a level $\mathfrak{n}$, a (parallel) weight $k\geq 2$ and a primitive ray class character $\chi$ modulo $\mathfrak{n}$. Then one can form the space $S_k(\mathfrak{n},\ch …
3 votes
0 answers
97 views

Tables of eigenvalues for Hilbert newforms of level $\mathfrak{p}$

Bit of a naïve question but are there tables of Hecke eigenvalues for Hilbert newforms over say real quadratic fields (of parallel weight not necessarily equal to 2 and level $\Gamma_0(\mathfrak{p})$) …
3 votes
0 answers
94 views

Representations of $\mathbb{H}^{\times}$ and $\mathbb{H}^{\times}/\mathbb{R}^{\times}$

In an attempt to recapture Eichler's theta correspondence I have hit a stumbling block. Let $D$ be a quaternion algebra over $\mathbb{Q}$, ramified at $p,\infty$. Also let $V_j = \text{Symm}^j(\math …