Nonlifts in S<sub>10</sub>(K(16))<sup>−</sup>

Nonlifts in S₁₀(K(16))⁻ are old forms

The two nonlift eigenforms in S₁₀(K(16))⁻ must be the two old forms coming from the two nonlift eigenforms in S₁₀(K(8))⁺. This already proves S₉(K(16))⁺ has at least two nonlift eigenforms and hence Borcherds products are not needed to help span this Fricke eigenspace.

Nonlifts in S10(K(16))− are old forms

Nonlifts in S₁₀(K(16))⁻ are old forms