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The database currently contains 368,356 Hilbert modular forms over 400 totally real number fields of degree 2 to 6. Here are some further statistics.

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By quadratic base field: \(\Q(\sqrt{2})\)   \(\Q(\sqrt{3})\)   \(\Q(\sqrt{5})\)   \(\Q(\sqrt{6})\)   \(\Q(\sqrt{7})\)   \(\Q(\sqrt{10})\)   \(\Q(\sqrt{11})\)   \(\Q(\sqrt{13})\)   \(\Q(\sqrt{14})\)   \(\Q(\sqrt{15})\)   $\cdots$
By cubic base field: $\Q(\zeta_7)^+$   $\Q(\zeta_9)^+$   3.3.148.1   3.3.169.1   3.3.229.1   3.3.257.1   3.3.316.1   $\cdots$
By quartic base field: 4.4.725.1   $\Q(\zeta_{15})^+$   $\Q(\sqrt{2},\sqrt{5})$   4.4.1957.1   $\Q(\zeta_{20})^+$   $\Q(\zeta_{16})^+$   4.4.2225.1  
By quintic base field: 5.5.14641.1   5.5.24217.1   5.5.36497.1   5.5.38569.1   5.5.65657.1   5.5.70601.1   $\cdots$
By sextic base field: 6.6.300125.1   $\Q(\zeta_{13})^+$   6.6.434581.1   $\Q(\zeta_{21})^+$   6.6.485125.1   6.6.592661.1   $\cdots$
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e.g. 2.2.5.1-31.1-a