Label of a Siegel modular form (awaiting review)

The label of a newform $f\in S_{\underline{k}}^{\rm new}(\Gamma_F(N),\chi)$ has the format \( g.F.N.k1...kd.a.x \), where

• \( g \) is the degree;

• \( F \) is the family;

• \( N \) is the level;

• \( \underline{k}=(k_1,\dots,k_d) \) 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 \(g.F.N.k1...kd.a.x.n.i\), 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 $\chi$.