ho.history overview - What is Shimura referring to by "an incorrect formula given by Minkowski... known to most experts."

I do not know where in the original sources, but the topic under discussion is the mass formula for integral quadratic forms. The accepted source with correct information is Conway and Sloane,

Low Dimensional Lattices. IV. The Mass Formula

Proceedings of the Royal Society of London, A 419, 259-286 (1988).

In the actual publication, the tables are sprinkled throughout, and I found it difficult to read the text. I have some sort of preprint around here where the tables are all at the end, easier to find what you want. But it still takes some real patience, and in fact some imagination, to use properly.

I can recommend the book by the same Conway and Sloane, called Sphere Packings, Lattices, and Groups.