There are many nutritional deficiencies that can cause low levels of thyroid hormones. Some of the important thyroid hormones are thyroid stimulating hormone (TSH) which stimulates your thyroid to make the hormone T4 which converts to the active form that your body can use, T3.
There are many different nutritional deficiencies that can affect both of these hormones such as magnesium, vitamin B12, iodine, zinc and protein. Because TSH is maintained by these specific nutrients, any inadequacies in these nutrients can and will affect the production of TSH. Examples of foods that support TSH production are be lentils, pumpkin seeds, spinach, almonds, and whole grains.
Accordingly, without the necessary nutrients your thyroid could actually have problems producing the T4 hormone or converting it to T3. T4 production is supported by foods high in iodine such as fresh vegetables, seaweed, kelp etc. Even foods high in selenium are great to add such as sunflower seeds, mushrooms and brazil nuts.
On the other hand there are foods that you should avoid is your thyroid function is low- foods that suppress thyroid functions are soy, cruciferous vegetables (they are healthy but they slow down iodine absorption therefore suppress thyroid hormones and coffee.