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Nonnegativity cutoffs for level-one modular forms

Paul Jenkins

Palomar Registrypalomar/PALOMAR-2026-09-25-000011Sep 25, 2026math.NTscore 0

A Lean formalization of the qualitative well-definedness of the nonnegativity Sturm bound A(k) for real level-one modular forms. For every weight k at least 12 and divisible by four, the formalization proves that a finite initial segment detects coefficientwise nonnegativity and that its optimal endpoint is attained as the greatest possible first negative Fourier-coefficient index.

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