It is going to depend upon what the variety is and your ultamate objective.

Variety dwarf Atropurpureum, objective remain a containerized plant. Jerry

You could stay in the 3gal by root pruning, wait until fall for that.
If potting up a 5 gal will hold a slow grower indefinitley with root prunning.

Here is a link that might be useful: root prunning

There is no such thing as a permanent container for a tree, unless it dies in that container. ;o)

How large a container needs to be, or CAN be, depends on the 3-way relationship between plant mass, container size, and soil type. We often concern ourselves with "over-potting" (using a container that is too large), but "over-potting" is a term that arises from a lack of basic knowledge about the 3-way relationship noted, which should logically determine appropriate container size(s).
It's often parroted that you should only move up one size in containers when "potting-up". The reasoning is the soil will remain wet too long and cause root rot issues, but it is the size/mass of the material and soil type/composition that determines both the upper & lower limits of appropriate container size - not consecutive volume progression.

Plants grown in slow soils need to be grown in containers with smaller soil volumes so that the plant can use water quickly, allowing air to return to the soil. This (smaller soil volumes) and the root constriction that accompanies it will cause plants to both extend branches and gain o/a mass much more slowly - a bane if rapid growth is the goal - a boon if growth restriction and a compact plant are what you have you sights set on.

Conversely, rampant growth can be had by growing in very large containers and in very fast soils where frequent watering and fertilizing is required - so it's not that trees rebel at being potted into very large containers per se, but rather, they rebel at being potted into very large containers with a soil that is too slow and water-retentive.

We know that there is an inverse relationship between soil particle size and the height of the PWT in containers. As particle size increases, the height of the PWT decreases, until at about a particle size of just under 1/8 inch, soils will no longer hold perched water. If there is no perched water, the soil is ALWAYS well aerated, even when the soil is at container capacity (saturated).

So, if you aim for a soil (like the gritty mix many @ GW are using) composed primarily of particles >1/16", there is no upper limit to container size. The lower size limit will be determined by the soil volume's ability to furnish water enough to sustain the plant between irrigations. Bearing heavily on this ability is the ratio of fine roots to coarse roots. It takes a minimum amount of fine rootage to support the canopy under high water demand. If the container is full of large roots, there may not be room for a sufficient volume of the fine roots that do all the water/nutrient delivery work and the coarse roots, too. You can grow a very large plant in a very small container if the root have been well managed and the lion's share of the rootage is fine.

Al