The label of a Maass newform $f \in M_k(\Gamma_0(N), \chi)$ either has the format $N.k.a.m.d$ or $N.m$, 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 Conrey label of the Dirichlet character $\chi$;
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$m$ is the spectral index, which uniquely identifies the eigenvalue $\lambda$ of $f$;
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$d$ indicates which form among those of level $N$, Dirichlet character $N.a$, and eigenvalue $\lambda$ this is.
The shorter form is used when $k=0$ and $a=1$ and $d=1$.
For squarefree level, it is conjectured that there is only one Maass form per eigenvalue $\lambda$, hence $d$ is (currently) always $1$. Generally, there are only finitely many Maass newforms in $M_k(\Gamma_0(N), \chi)$ with the same eigenvalue $\lambda$. Then $d$ denotes the index among these finitely many forms, where the ordering is lexicographical in the sequence $\{ \bigl(\mathrm{Re}(a(n)), \mathrm{Im}(a(n))\bigr) \}_{n \geq 1}$.