Each embedding $\iota\colon \Q(f)\to \C$ gives rise to a modular form $\iota(f)$ with $q$-expansion $\sum \iota(a_n)q^n$; the modular form $\iota(f)$ is an embedding of the newform $f$.
If $f$ is a newform of character $\chi$, each embedding $\Q(f)\to \C$ induces an embedding $\Q(\chi)\to \C$ of the value field of $\chi$. The embeddings of $f$ may be grouped into blocks with the same Dirichlet character; distinct blocks correspond to modular forms with distinct (but Galois conjugate) Dirichlet characters.
- Review status: reviewed
- Last edited by Andrew Sutherland on 2018-12-07 21:17:35
- 2018-12-07 21:17:35 by Andrew Sutherland (Reviewed)