An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus
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| Format: | Preprint |
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2025
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| _version_ | 1866909928914944000 |
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| author | Banerjee, Debargha Airon, Dron Vishwakarma, Pranjal Debnath, Ronit |
| author_facet | Banerjee, Debargha Airon, Dron Vishwakarma, Pranjal Debnath, Ronit |
| contents | 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 $k \leq 4$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus Banerjee, Debargha Airon, Dron Vishwakarma, Pranjal Debnath, Ronit Number Theory 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 $k \leq 4$). |
| title | An algorithm to compute upper bounds of dimensions for Siegel Modular Forms of Prime Level and Arbitrary Nebentypus |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.22207 |