Newspaces with nebentypus: an explicit dimension formula, classification of trivial newspaces, and character equidistribution property
E Ross - arXiv preprint arXiv:2407.08881, 2024 - arxiv.org
Consider $ N\geq 1$, $ k\geq 2$, and $\chi $ a Dirichlet character modulo $ N $ such that
$\chi (-1)=(-1)^ k $. For any bound $ B $, one can show that $\dim S_k (\Gamma_0 …
$\chi (-1)=(-1)^ k $. For any bound $ B $, one can show that $\dim S_k (\Gamma_0 …
Computing classical modular forms
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Dimension formulas for Siegel modular forms of level 4
We prove several dimension formulas for spaces of scalar‐valued Siegel modular forms of
degree 2 with respect to certain congruence subgroups of level 4. In case of cusp forms, all …
degree 2 with respect to certain congruence subgroups of level 4. In case of cusp forms, all …
On the number of Galois orbits of newforms
LV Dieulefait, AM Pacetti, P Tsaknias - 2021 - content.ems.press
Counting the number of Galois orbits of newforms in Sk (0 (N)) and giving some arithmetic
sense to this number is an interesting open problem. The case N= 1 corresponds to Maeda's …
sense to this number is an interesting open problem. The case N= 1 corresponds to Maeda's …
Counting modular forms by rationality field
A Cowan, K Martin - arXiv preprint arXiv:2301.10357, 2023 - arxiv.org
We investigate the distribution of degrees and rationality fields of weight 2 newforms. In
particular, we give heuristic upper bounds on how often degree $ d $ rationality fields occur …
particular, we give heuristic upper bounds on how often degree $ d $ rationality fields occur …
Counting locally supercuspidal newforms
A Knightly - arXiv preprint arXiv:2310.17047, 2023 - arxiv.org
We set up a simple trace formula giving the number of holomorphic newforms of weight $ k $
and level $ M $ whose local representation type at each $ p| M $ is a fixed supercuspidal …
and level $ M $ whose local representation type at each $ p| M $ is a fixed supercuspidal …
An on-average Maeda-type conjecture in the level aspect
K Martin - Proceedings of the American Mathematical Society, 2021 - ams.org
We present a conjecture on the average number of Galois orbits of newforms when fixing the
weight and varying the level. This conjecture implies, for instance, that the central $ L …
weight and varying the level. This conjecture implies, for instance, that the central $ L …
Root number bias for newforms
K Martin - Proceedings of the American Mathematical Society, 2023 - ams.org
Previously we observed that newforms obey a strict bias towards root number $+ 1$ in
squarefree levels: at least half of the newforms in $ S_k (\Gamma _0 (N)) $ with root number …
squarefree levels: at least half of the newforms in $ S_k (\Gamma _0 (N)) $ with root number …
Dimensions of paramodular forms and compact twist modular forms with involutions
T Ibukiyama - arXiv preprint arXiv:2208.13578, 2022 - arxiv.org
The dimension formula for algebraic modular forms of any weight associated with the binary
quaternion hermitian maximal lattices in non-principal genus has been known by our …
quaternion hermitian maximal lattices in non-principal genus has been known by our …
Dimension formulas of modular form spaces with character for Fricke groups
Y Zhang, Y Zhou - arXiv preprint arXiv:2211.09509, 2022 - arxiv.org
arXiv:2211.09509v1 [math.NT] 17 Nov 2022 Page 1 arXiv:2211.09509v1 [math.NT] 17 Nov
2022 DIMENSION FORMULAS OF MODULAR FORM SPACES WITH CHARACTER FOR …
2022 DIMENSION FORMULAS OF MODULAR FORM SPACES WITH CHARACTER FOR …