The effect of the trace operator on the duality of modular grids in genus zero levels
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 0(N) of genus zero and show exactly when duality still holds after applying the trace operator.
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