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Let $E_8$ be the unique unimodular positive definite even integral symmetric form of rank 8. Let $[1]$ denote the unique unimodular positive definite even integral symmetric form of rank 1. Is $E_8 \oplus m[1]$ ever diagonalizable for any $m \geq 1$?

This question for me is motivated by thinking about intersection forms of 4-manifolds - hence the tag.

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