A better way is to use a Notch Filter at 40MHz but you cannot escape from its' harmonics.
Using cascaded notches ( 40MHz,80MHz,120MHz etc.) will attenuate the signal as it can..
If you want a clean 40MHz signal it is best to generate one as near a sine wave as possible then use minimal filtering to eliminate harmonics. If you want to start with a 'dirty' 40MHz you will need far more complex filtering and you will end up with a much more complicated circuit.
You should also be aware that harmonics appear at multiples of the fundamental frequency. so for a 40MHz oscillator they will be at 80MHz, 120MHz, 160MHz and so on. If you are seeing other frequencies it is probably because the module starts internally at a lower frequency and multiplies it up to 40MHz with some of those lower frequencies leaking out.
As I pointed out, those modules are designed for driving digital circuits where the only consideration is that the waveform exceeds the logic input thresholds, how clean it is doesn't really matter. They are not intended for use as transmitter signal sources.
Well, let me try to understand the other way: it can be more fun sometimes.
Your base frequency is 40 MHz; let me assume that this is correct but the waveform is not sinusoidal. Then you will have also components of 80, 120, 160, 200 MHz etc.
If the waveform is dirty (noisy), you will have all frequencies from DC to inf.
If your waveform is modulated, you will have only 40+/- Alpha MHz.
Assume further that your filter is a single stage 3db/oct slope. This (your BP filter) is same as two filters in series: one high pass and one low pass.
Now you can see how your waveform will pass through the filter.
Suppose you are modulating the 40MHz with 20KHz audio. The filter will scarcely touch it.
Best is to start with clean stuff; you will have less headaches later.
Reviewing the thread from the start, I don't know if you are asking about a 40 or 100 MHz crystal oscillator? Modulation has been mentioned, but unclear which kind and how it's achieved. Is it a frequency modulated oscillator?
Sounds like you want to use the oscillator as radio transmitter, if so, it should keep usual requirements for harmonics and spurious signals, e.g. at least 40 dB suppression of harmonics.