Defining parameters
Level: | \( N \) | = | \( 8 = 2^{3} \) |
Weight: | \( k \) | = | \( 14 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(56\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 29 | 17 | 12 |
Cusp forms | 23 | 15 | 8 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)
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 |
---|---|---|---|---|
8.14.a | \(\chi_{8}(1, \cdot)\) | 8.14.a.a | 1 | 1 |
8.14.a.b | 2 | |||
8.14.b | \(\chi_{8}(5, \cdot)\) | 8.14.b.a | 2 | 1 |
8.14.b.b | 10 |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)