The label of a newform $f\in S_k^{\rm new}(N,\chi)$ has the format \( N.k.a.x \), where
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\( N\) is the level;
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\(k\) is the weight;
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\(N.a\) is the label of the Galois orbit of the Dirichlet character $\chi$;
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\(x\) 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
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\(n\) determines the Conrey label \(N.n\) of the Dirichlet character \(\chi\);
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\(i\) is an integer ranging from 1 to the relative dimension of the newform that distinguishes embeddings with the same character $\chi$.