A characterization of ordinary modular eigenforms with CM
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arXiv
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| Format: | Preprint |
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2012
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| _version_ | 1866909870155890688 |
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| author | Adibhatla, Rajender Tsaknias, Panagiotis |
| author_facet | Adibhatla, Rajender Tsaknias, Panagiotis |
| contents | For a rational prime $p \geq 3$ we show that a $p$-ordinary modular eigenform $f$ of weight $k\geq 2$, with $p$-adic Galois representation $ρ_f$, mod ${p^m}$ reductions $ρ_{f,m}$, and with complex multiplication (CM), is characterized by the existence of $p$-ordinary CM companion forms $h_m$ modulo $p^m$ for all integers $m \geq 1$ in the sense that $ρ_{f,m}\sim ρ_{h_m,m}\otimesχ^{k-1}$, where $χ$ is the $p$-adic cyclotomic character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1206_0177 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | A characterization of ordinary modular eigenforms with CM Adibhatla, Rajender Tsaknias, Panagiotis Number Theory 11F33, 11F80 For a rational prime $p \geq 3$ we show that a $p$-ordinary modular eigenform $f$ of weight $k\geq 2$, with $p$-adic Galois representation $ρ_f$, mod ${p^m}$ reductions $ρ_{f,m}$, and with complex multiplication (CM), is characterized by the existence of $p$-ordinary CM companion forms $h_m$ modulo $p^m$ for all integers $m \geq 1$ in the sense that $ρ_{f,m}\sim ρ_{h_m,m}\otimesχ^{k-1}$, where $χ$ is the $p$-adic cyclotomic character. |
| title | A characterization of ordinary modular eigenforms with CM |
| topic | Number Theory 11F33, 11F80 |
| url | https://arxiv.org/abs/1206.0177 |