It depends totally on the amount and type of programming you are required to do and the amount and type of managerial duties you have to perform.
Being a manager means lots of interruptions, changes of tack and things like meetings etc.
If your programming is "limited" to small pieces of non urgent work then you can fit these in around your managerial duties. If you need to spend significant amounts of "quality" time on a programming task then you aren't going to get that time due to your managerial responsibilities.
If your team is large and/or complex then you are going to need to spend more time managing than you would if it were a small team dedicated to one one or two products/projects. You'll find that you just don't have the time to do any meaningful programming - even on small tasks.
In a previous job I had this role and it worked for me because I kept my programming tasks small. It actually worked to our advantage.
Firstly, I could assess all the requests that came in and if they were small add them to my queue (which was always short) or get back to the client (in this case another manager) with a more accurate timescale for when the work would be done.
Secondly it meant that the developers on the team weren't getting constantly pulled off their current work to fix minor bugs or do small enhancements.
Thirdly, the clients were happy as their urgent problems were fixed fairly rapidly.
It kept me in touch with the code base so I could have meaningful conversations with my team about problems and with my managers and clients about timescales without having to get the team involved all the time.