Part 107 UAS pilot reported flying in controlled airspace with verbal authorization. They learned after the flight that written authorization was needed.

Narrative

On day 0; I flew an UAS over an agriculture field to spray fungicide on the corn. The max flight height was 20 feet AGL. This field was south of HUF airport. I submitted three waivers on Drone Zone to seek permission. After submission; weeks before; I had not heard back; as this was my first time dealing with drone zone; I did not know if I was going to hear back. I called HUF tower the evening before the flight asking if they had received my waivers and if I was able to fly. Tower said they needed to send my information to the supervisor; and they would get back with me. Later that evening I received a call from the supervisor stating I was all good to go for tomorrow; only that I needed to call 15 minutes prior to my flight. That next morning; I called tower letting them know I would be flying in the next 30 minutes; and they again said I was all good to go. Therefore; I continued with my operation; and sprayed the field.I did not know; I did not have approval for the field I was flying over; but only had approval for the field south of that one and there was a miscommunication when I spoke to tower asking if I was all approved. At the time; I had no idea I was breaking a FAR by flying the drone in a class Delta that I did not have approval for.I have now been informed that I am supposed to get an email with the approval; not just a verbal approval from tower. I will now make sure I receive the approval via email before contacting tower or any flight operation.