An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus
Number Theory
2025-12-01 v1
Abstract
We describe an algorithmic method to determine the image of restriction maps for Siegel modular forms with \textit{arbitrary} characters and arbitrary weight. A program has been implemented in the mathematical software \texttt{Java} to compute the Fourier expansion of the image of these restriction maps for Siegel modular forms of genus two. This approach allows us to compute an upper bound for the space of Siegel modular forms with {\it non-trivial} character (which has not been previously known) and arbitrary weights (including low weight ).
Cite
@article{arxiv.2511.22207,
title = {An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus},
author = {Debargha Banerjee and Dron Airon and Pranjal Vishwakarma and Ronit Debnath},
journal= {arXiv preprint arXiv:2511.22207},
year = {2025}
}