Defining parameters
Level: | \( N \) | = | \( 8 = 2^{3} \) |
Weight: | \( k \) | = | \( 16 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(64\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 33 | 20 | 13 |
Cusp forms | 27 | 18 | 9 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(8))\)
We only show spaces with even 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 |
---|---|---|---|---|
8.16.a | \(\chi_{8}(1, \cdot)\) | 8.16.a.a | 1 | 1 |
8.16.a.b | 1 | |||
8.16.a.c | 2 | |||
8.16.b | \(\chi_{8}(5, \cdot)\) | 8.16.b.a | 14 | 1 |
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)