Hi there "mrmakas", and welcome!
My plans are to put in a carpet covering the dirty concrete floor,
In general, carpet is a bad idea for a studio: It leaved the room sounding "honky" and dull. Think of it this way: How many professional studios do you see with carpet all over the floor?

There's a reason for that.... Actually there are several reasons for that. So if the pros don't do it, then probably you shouldn't do it either.
If your concrete floor is in bad shape, then I would suggest laying laminate flooring in it, instead of carpet. Laminate flooring is almost as good as concrete, and looks great too. Another option would be ceramic tile flooring, which is also very good.
i was planing on building helmholz resonator-type ceiling mounted bass absorbers,
Helmholtz devices are very, very difficult to tune. Nowhere near as easy as the text books say. Before you can build them, you would first need to build the room and accurately measure the modal response, so that you can determine exactly what frequencies you need to address. That's already very hard to do, due to the laws of physics: measuring low frequencies is complicated and inaccurate, and modal ringing occurs at very tight, precise frequencies (high Q). So there is no guarantee that you would be able to determined exactly what the frequencies are. And even if you did manage to do that, you would then have to design a resonator tuned to that exact frequency, and it would have to have enough internal volume to be able to absorb the energy efficiently. You need at least 1% of the room volume for each such device. Finally, you say you want to put those devices on the ceiling, but what if the mode you need to treat is not associated with the ceiling? Helmholtz resonators are pressure-based, so they must be located at the pressure node for the standing wave that is causing the problem. If the pressure node happens to be on the back wall, or the side wall, then it is no use at all putting the device on the ceiling.
So I would say: forget tuned resonant traps for bass. Just go with ordinary broad-band absorption.
This was according to a book that i am reading, where they are building a similar size studio.
And the book says to treat the room with carpet on the floor and Helmholtz resonators on the ceiling???

Here's some advice about that book: throw it away. Buy a real book about real acoustics, written by a real acoustician. In fact, I'd suggest two books: "Master Handbook of Acoustics" by F. Alton Everest (that's sort of the Bible for acoustics), and "Home Recording Studio: Build it Like the Pros", by Rod Gervais. The first book will teach you what you need to know about acoustics, and it was written by one of the most respected acousticians of modern times. The second book will teach you how to actually design and build the treatment for your room.
Are the counteracting ceiling panels a good idea?
No. The normal way of doing studios is with a hard, reflective floor, and a soft absorptive ceiling.
so far i had only heard about the corner traps to be used in small room bass control.
Right. All rooms need bass trapping, and small rooms need a LOT of bass trapping. The smaller it is, the more it needs.
Mixing is the sole purpose of the room.
Great. So it is just a control room, and needs no isolation. How do you have your current room set up at present? What speakers? Where are they located? It would be good if you could do an accurate diagram of the new room (in SketchUp), and post it here, and also post a couple of photos of that room.
I typed in the room measurements into BobGolds.com room mode calculator, and there seems to be a nasty bumb at around 65Hz. Do not wish to have to bother with that in my mixes
That's just one of many problems: The room is based on a square! 2.5 m high, and 5m long. Therefore, all of the second-order modes for height line up perfectly with the first order modes for length. That's a big problem. That needs to be fixed.
- Stuart -