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I've never used Gaia passbands, or any type of passbands before for that matter. I have a theoretical model of a stellar object, and its corresponding emissions as a function of wavelength. I'd like to find the coordinates of the object on the Gaia's HR diagram that uses G, Gbp-Grp coordinates. I downloaded the passbands, which appear to be long arrays, that when plotted versus wavelength certainly return the filters on the Gaia website. My problem is, I'm not sure how to use these passbands. Do I multiply the filters with my emissions and integrate? Reading online, I was instructed to convolate my emissions with the passbands, but this would return to me another array, not a real number. I'd appreciate any guidance on this matter, as online everyone seems to tell you what to do, but doesn't really give any clear steps on how to do so. Maybe I'm just looking at the wrong places.

I'm by no means an astronomer, I'd just like to know where my object would lie on the HR diagram. Thanks for the understanding.

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You should multiply your spectrum by the filter response function, integrate to get a flux and then turn that into a magnitude using a published zero-point flux (i.e. the flux that defines a magnitude of zero). I can't see where a mathematical convolution comes into it.

Remember to modify your theoretical spectrum for any interstellar extinction.

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