ADXL345 interference at 64Hz and its multiples

Good Evening, 

Currently for my project I'm using ADXL345 sensor, connected to Arduino Nano Board, powered by a 9V battery, communicating with pc trought Bluetooth connection at 115200 baud/s.

Setting the sampling frequency on high values (1600/3200, but espetially 1600) I get some very regular disturbances with same amplitude at 64 Hz and its precise multiples (128, 192... until available bandwidth).

In the annexes there is the spectrum of a signal (peaks not at the previously mentioned frequences are supposed to be there), sampling freq 1600Hz, 10s of acquisition

Have you ever experienced something similar? do you have any idea what it could be?