Force 4K in Windows 7 (wrong max resolution reported by the TV)

I have a computer I want to use as a media center running Windows 7 on an AMD Radeon HD 6870. I have a 55" 4K TV (and 4K works, a small Android TV box runs in 4K on it).

The problem is that it's a cheap brand TV and apparently the engineers who built it forgot to change the reported max resolution to 4K... The model reported is ELUFT551, which is a 2014 55" 1080p TV. So obviously, my computer doesn't let me choose 4K as a resolution (max 1080p).

What I'm looking for is a way to either spoof the reported max resolution or force a custom resolution.

Is there a way to do this?

Answer

I finally found a way to achieve this. Here's how to do it :

First, you need to patch the HDMI Pixel Clock on the card with this utility : http://www.monitortests.com/forum/Thread-AMD-ATI-Pixel-Clock-Patcher

Then, once it's done and the computer has been rebooted, you use Custom Resolution Utility (http://www.monitortests.com/forum/Thread-Custom-Resolution-Utility-CRU) to add the desired resolution to the available resolutions list.

I'm not sure if a reboot is necessary here, but then I was able to see the 3840x2160 resolution in the Windows display settings!