Labels for classical modular forms

The label of a newform $f\in S_k^{\rm new}(N,\chi)$ has the format $N.k.a.x$, where

• $N$ is the level;

• $k$ is the weight;

• $N.a$ is the label of the Galois orbit of the Dirichlet character $\chi$;

• $x$ is the label of the Galois orbit of the newform $f$.

For each embedding of the coefficient field of $f$ into the complex numbers, the corresponding modular form over $\C$ has a label of the form $N.k.a.x.n.i$, where

• $n$ determines the Conrey label $N.n$ of the Dirichlet character $\chi$;

• $i$ is an integer ranging from 1 to the relative dimension of the newform that distinguishes embeddings with the same character $\chi$.