We extend Prasad's results on the existence of trilinear forms on representations of GL2 of a local field, by permitting one or more of the representations to be reducible principal series, with infinite-dimensional irreducible quotient. We apply this in a global setting to compute (unconditionally) the dimensions of the subspaces of motivic cohomology of the product of two modular curves constructed by Beilinson.
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Michael Harris, Anthony J. Scholl, A note on trilinear forms for reducible representations and Beilinson's conjectures. J. Eur. Math. Soc. 3 (2001), no. 1, pp. 93–104DOI 10.1007/S100970000026