Abstract: A new database by Bergstrom, Faber and van der Geer lists dimensions of spaces of Siegel modular forms for $\Gamma(2)$ according to their $S_6$-types. We explain how to "diagonalize" the database in order to obtain a large list of automorphic representations with ramification at $p=2$. The natural density of the irreducible characters of $S_6$ gives rise to a density of local representations at $p=2$ as the weight tends to infinity. After calculating the Plancherel measure for the relevant local representations, the results turn out to be consistent with the "automorphic Plancherel density theorem" proven by Sug Woo Shin.
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