using a symmetrical sinusoidal PWM produces odd harmonics only. If you have a dc offset in the reference or the carrier, then the output voltage will contain even and odd harmonics.
The output voltage in a 3-level inverter contains harmonics at the switching frequency. However, multiple harmonics are also present at the switching frequency.
Considering that the output voltage has no offset. A simulation of the inverter can be a quick way of seeing that harmonics contains the output voltage.
I have simulated three phase, three level inverter in SIMULINK and getting even harmonics in line voltage. My thought is , when sine is an odd symmetrical waveform, why the even harmonics are appearing. In the output voltage spectrum the dominant harmonics are n-2 and n+2 where n=fc/fm
Ideally, for the case when the voltage at the output of the inverter has no offset you have only odd harmonics, grouped in families. These families are placed symmetrically, left and right, with respect to ratios between the carrier frequency and the modulator frequency if this ratio is an integer. For numerical PWM, things are a little bit more complicated and I recommend Bose Edition 2006. Have a great day.