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arXiv · 2406.00173

The effect of the trace operator on the duality of modular grids in genus zero levels

Archer Clayton·Paul Jenkins
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Abstract

Griffin, the second author, and Molnar studied coefficient duality for canonical bases for a broad range of spaces of weakly holomorphic modular forms, showing that the Fourier coefficients of canonical basis elements appear as negatives of Fourier coefficients for elements of a canonical basis of a related space of forms. We investigate the effect of the trace operator on this duality for modular forms for $\Gamma_0(N)$ of genus zero and show exactly when duality still holds after applying the trace operator.

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Archer Clayton, Paul Jenkins. 2024-05-31. The effect of the trace operator on the duality of modular grids in genus zero levels. https://arxiv.org/abs/2406.00173

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