Assuming that in the OTP scheme, the key has more values than the alphabet, then: using modular math predetermines that the highest possible value in the ciphertext will reveal the modulus used in the scheme.
Therefore, ciphertext reveals highest possible modulus.
Put more simply, given enough ciphertext, ciphertext reveals modulus.
Am I correct?
Edit: clarification: now that I think more about it, the key or its space size in relation to the alphabet size/plaintext size does not even matter. If the One Time Pad uses modular math in its scheme, then the ciphertext reveals the modulus, without exception. Looking for either confirmation or rejection here. Thank you.