### Abstract

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by $\mathbb{Q}(\sqrt{-3})$ and the other by $\mathbb{Q}(\sqrt{-2})$. The values of the $p$-th Fourier coefficients of all the forms in each family can be described by a single formula, which we provide explicitly. This allows us to establish a formula relating the $p$-th Fourier coefficients of forms of different weights, within each family. We then prove congruence relations between the $p$-th Fourier coefficients of these newforms at all odd weights and values coming from two of Zagier's sporadic Ap{\'e}ry-like sequences.

Original language | English |
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Pages (from-to) | 12 pages |

Journal | Research in Number Theory |

DOIs | |

State | Published - Mar 2019 |

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## Cite this

McCarthy, D., Gomez, A., & Young, D. (2019). Apéry-like numbers and families of newforms with complex multiplication.

*Research in Number Theory*, 12 pages. https://doi.org/10.1007/s40993-018-0145-7