We give some relations between the weights and the prime p of elements of the mod p kernel of the generalized theta operator Θ [j] . In order to construct examples of the mod p kernel of Θ [j] from any modular form, we introduce new operators A (j) (M ) and show the modularity of F |A (j) (M ) when F is a modular form. Finally, we give some examples of the mod p kernel of Θ [j] and the filtrations of some of them.
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