And even lower, private room in Sleep Cheap Hostel was only €31 and not far from Artemis.
I just check the Sleep Cheap Hostel over a week time span. Indeed it varies from £32.20 to £38.64.
However their room is 4 beds private room. This sort of room is intended for a group of 4 people wanting to stick together in one room, not really designed for a single traveller.
Of course a single traveller could still book it but not worthy. You avoid this sort of room as you pay a single private room in a hostel, but the environment / decoration in the room is not for a single room, you will still see bunks of 4 sets single beds or two double decks beds. The only different is you are the only occupant in the room. To make your money worthy you will be looking for a private room similar to the room in a hotel, e.g with single or double beds.
If you look at Trivago, Booking.com, hotel.de you sometimes could still find a pension for EUR30 pn, but you have got to be lucky to get it as it is not necessary fits to the dates you are staying in Berlin.