Nonlifts in S<sub>9</sub>(K(16))<sup>+</sup>

Nonlifts in S₉(K(16))⁺ are old forms

The one nonlift eigenform in S₉(K(16))⁺ must be the old form coming from the nonlift eigenform in S₉(K(8))⁻. This already proves S₉(K(16))⁺ has at least one nonlift eigenform and hence Borcherds products are not needed to help span this Fricke eigenspace.

Nonlifts in S9(K(16))+ are old forms

Nonlifts in S₉(K(16))⁺ are old forms