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In this short paper we generalise a result of Diamond--Sasaki connectinggeometric modularity of algebraic weights to geometric modularity ofnon-algebraic weights and vice versa. In particular, we show that geometricmodularity of non-algebraic weights implies geometric modularity of multiplealgebraic weights, which is easy to see. More significantly, we show thatgeometric modularity of multiple algebraic weights sometimes implies geometricmodularity of a non-algebraic weight. This connects work of Diamond--Sasaki toearlier work on generalisations of the weight part of Serre's conjecture.

Geometric modularity for algebraic and non-algebraic weights