Nonlifts in S<sub>11</sub>(K(8))<sup>+</sup>

Nonlifts in S₁₁(K(8))⁺ are old forms

The one nonlift eigenform in S₁₁(K(8))⁺ must be the old form coming from the nonlift eigenform in S₁₁(K(4))⁻. This already proves S₁₁(K(8))⁺ has at least one nonlift eigenform and hence Borcherds products are not needed to help span this Fricke eigenspace.

Nonlifts in S11(K(8))+ are old forms

Nonlifts in S₁₁(K(8))⁺ are old forms