Expressions for weight 2 cusp forms in holomorphic eta quotients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913420940410880 |
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| author | Chan, Elisabeth Combes, Lewis |
| author_facet | Chan, Elisabeth Combes, Lewis |
| contents | We attempt to compute expressions in terms of the Dedekind eta function for all weight 2 new cusp forms with level up to 100, using methods of Allen et. al. In cases where no expression exists, we raise the level instead of the weight, meaning our eta quotients are always holomorphic. Of the forms we examine, we find expressions for all but 4. We also present methods to find expressions with relatively few terms, and how these expressions can be used to demonstrate zeroes of modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05748 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expressions for weight 2 cusp forms in holomorphic eta quotients Chan, Elisabeth Combes, Lewis Number Theory 11F03, 11F20, 11Y40 We attempt to compute expressions in terms of the Dedekind eta function for all weight 2 new cusp forms with level up to 100, using methods of Allen et. al. In cases where no expression exists, we raise the level instead of the weight, meaning our eta quotients are always holomorphic. Of the forms we examine, we find expressions for all but 4. We also present methods to find expressions with relatively few terms, and how these expressions can be used to demonstrate zeroes of modular forms. |
| title | Expressions for weight 2 cusp forms in holomorphic eta quotients |
| topic | Number Theory 11F03, 11F20, 11Y40 |
| url | https://arxiv.org/abs/2407.05748 |