  Using wreath products, we construct a finitely generated pro-p group G with
infinite normal Hausdorff spectrum with respect to the p-power series. More
precisely, we show that this normal Hausdorff spectrum contains an infinite
interval; this settles a question of Shalev. Furthermore, we prove that the
normal Hausdorff spectra of G with respect to other filtration series have a
similar shape. In particular, our analysis applies to standard filtration
series such as the Frattini series, the lower p-series and the modular
dimension subgroup series.
  Lastly, we pin down the ordinary Hausdorff spectra of G with respect to the
standard filtration series. The spectrum of G for the lower p-series displays
surprising new features.
