You should charge as much as you can charge while still getting work. For fully remote work as a programmer, honestly, it tends to top out at $45/hour for experienced people. If you aren't experienced yet, you can't charge as much. This is because there's basically infinite workers willing to work in Europe on programming at that price.

For someone who can meet in person in the US, on site, with a legal ability to work and then works remotely you can do double that. For someone on site rates easily reach $200/hour and above. My Dad used to bill $213/hour doing neural network programming for credit card companies. Generally you spend Monday-Thursday on site consulting, often expensing a hotel, then head home for the weekend.