Just a simple question and the answer is probably no, but am I allowed to transmit a picture using SSTV on an FM 2 meter or 70 centimeter repeater?
I am in the United States.
Depends on the band plan and the repeaters operator. You wouldn't be violating any FCC rules, though, but if you're outside the US the answer may be different.
To expand on this, you are allowed to transmit any permitted mode on any permitted frequency your license is good for. That frequency and mode happening to correspond to an open repeater another station operates does not preclude you from making your transmission.
However, as a licensee, you've agreed to cooperate with other operators to make the most efficient use of the spectrum provided. This means that unless you have good reason to, or have coordinated with others, you generally follow the band plans in effect in your region.
Generally the band plans keep voice repeater and SSTV operations in separate frequencies. However the band plan is a way to coordinate effort, and not a rigid standard. As shown in this question, there are may groups that regularly use repeaters to send SSTV signals.
If the repeater is regularly used by other operators for voice, or is in service to a community for emergency operations, weather spotting, or other frequent uses, you'd probably be better off not tying it up with SSTV images. It'll be really annoying to those that keep their HT on all the time to hear the SSTV coming through.
If it's a quiet repeater and happens to be in an SSTV portion of the band plan, I wouldn't even bother asking, just go ahead and send and see what the response, if any, is.
If it's outside the SSTV band plan, but appears to be an underutilized repeater, it's your call. Asking might result in people saying 'no' without good reason, but doing it without getting explicit permission may irritate some. It may also intrigue others.
But, being honest with yourself, consider the question, "Who is likely to be listening to this repeater with an SSTV receiver?" If you're communicating specifically with someone who is set up to receive your images, direct communications isn't reasonable, and the repeater appears to be open and available for community use, I'd say go for it. If you're just sending random images to no one in particular, though, or merely experimenting with the mode, you probably don't need to use the repeater to accomplish your goals.
Just adding to the above answer: If you are going to transmit SSTV on a repeater that is also used for voice, you should try to be a courteous as possible:
Also, if the repeater is retransmitting on SSB you really should contact the operator first before transmitting SSTV. Remember, SSTV transmitted on SSB is considered full duty-cycle. While the SSB output on a well-engineered repeater will have no problems, others might not.
This is an issue we deal with all the time here. Currently we are seeking to expand county coverage for our SSTV and Data net with a repeater. Always ask the repeater trustee first. Always. Here we got a no from all the local repeaters. Here is why the local club repeater trustee said no. Most repeaters cannot handle the constant 100% duty cycle. That means repeater finals getting hot. Our net established guidelines for using a repeater. Only transmit pictures that are less than 1 minute in duration Scottie 2 is our preferred mode for simplex. If you are going to be operating a lot at one time use Robot modes. Robot 36 gives great color images. Stay Simplex as much as possible. Set your radio to low power or 1/2 maximum power to keep it from getting hot too. Most of the time you will not need a repeater if you have good antennas at least 20 ft elevation.