### Abstract

We consider the set of classical newforms with rational coefficients and no complex multiplication. We study the distribution of quadratic twist-classes of these forms with respect to weight k and minimal level N. We conjecture that for each weight k≥ 6 , there are only finitely many classes. In large weights, we make this conjecture effective: in weights 18 ≤ k≤ 24 , all classes have N≤ 30 ; in weights 26 ≤ k≤ 50 , all classes have N∈ { 2 , 6 } ; and in weights k≥ 52 , there are no classes at all. We study some of the newforms appearing on our conjecturally complete list in more detail, especially in the cases N= 2 , 3, 4, 6, and 8, where formulas can be kept nearly as simple as those for the classical case N= 1.

Original language | English (US) |
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Pages (from-to) | 835-862 |

Number of pages | 28 |

Journal | Ramanujan Journal |

Volume | 46 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1 2018 |

### Keywords

- Level
- Maeda conjecture
- Modular form
- Newform
- Weight

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## Cite this

*Ramanujan Journal*,

*46*(3), 835-862. https://doi.org/10.1007/s11139-017-9914-5