### Abstract

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by Q(-3) and the other by Q(-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 Apéry-like sequences.

Original language | English |
---|---|

Article number | 5 |

Journal | Research in Number Theory |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2019 |

## Fingerprint Dive into the research topics of 'Apéry-like numbers and families of newforms with complex multiplication'. Together they form a unique fingerprint.

## Cite this

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

*Research in Number Theory*,*5*(1), [5]. https://doi.org/10.1007/s40993-018-0145-7