The odd part of the intersection matrix of J
0
(N).
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Enter a
semicolon-separated
list of pairs [N,k] to obtain the odd intersection matrix for weight-k modular symbols of level N. You can also enter a single integer, in which case the weight k is automatically set equal to 1. When k=2, the intersection matrix is obtained as follows. Let A
1
, A
2
, ..., A
n
be the abelian subvarieties of J
0
(N) corresponding to newform classes of some level dividing N. This list is ordered so that ... The diagonal entries of the odd intersection matrix are zero, and the nondiagonal (i,j) entry is the odd part of the order of the intersection of the abelian varieties A
i
and A
j
.
WARNING:
The odd intersection matrix, which is square, is currently stored in the database as a flattened list, e.g., [a11, a12, a13, a21, a22, a23, a31, a32, a33].
I have computed this intersection matrix for many square-free integers N up to 2500. Click the "List Known Levels" button below to see exactly what I've computed.
Output format:
HUMAN
MAGMA