Defining parameters
Level: | \( N \) | = | \( 83 \) |
Weight: | \( k \) | = | \( 13 \) |
Nonzero newspaces: | \( 2 \) | ||
Sturm bound: | \(7462\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(83))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3485 | 3485 | 0 |
Cusp forms | 3403 | 3403 | 0 |
Eisenstein series | 82 | 82 | 0 |
Trace form
Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(83))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
83.13.b | \(\chi_{83}(82, \cdot)\) | 83.13.b.a | 1 | 1 |
83.13.b.b | 2 | |||
83.13.b.c | 80 | |||
83.13.d | \(\chi_{83}(2, \cdot)\) | n/a | 3320 | 40 |
"n/a" means that newforms for that character have not been added to the database yet