However, I’ll give you some freebie advice, try using Mosek as solver if you can (not sure about problem size, though). Maybe also think about which norms you want or need squared, and don’t square them unless necessary (certainly not needed for norm fro constraint).
Here is what this would look like in CVX. Use square_pos around norm_nuc if you want that squared. I didn’t square the norm fro in the constraint, which (squaring) serves no purpose (rather, apply sqrt to RHS, which in this case remains 1).