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- W4299622532 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 $k geq 6$, there are only finitely many classes. In large weights, we make this conjecture effective: in weights $18 leq k leq 24$, all classes have $N leq 30$, in weights $26 leq k leq 50$, all classes have $N in {2,6}$, and in weights $k geq 52$, 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 $N=1$." @default.
- W4299622532 created "2022-10-02" @default.
- W4299622532 creator A5082064002 @default.
- W4299622532 date "2016-11-21" @default.
- W4299622532 modified "2023-09-24" @default.
- W4299622532 title "Newforms with rational coefficients" @default.
- W4299622532 doi "https://doi.org/10.48550/arxiv.1611.06967" @default.
- W4299622532 hasPublicationYear "2016" @default.
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