Defining parameters
Level: | \( N \) | = | \( 8 = 2^{3} \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 7 | 8 |
Cusp forms | 9 | 5 | 4 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
8.7.c | \(\chi_{8}(7, \cdot)\) | None | 0 | 1 |
8.7.d | \(\chi_{8}(3, \cdot)\) | 8.7.d.a | 1 | 1 |
8.7.d.b | 4 |
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)