Defining parameters
Level: | \( N \) | = | \( 8 = 2^{3} \) |
Weight: | \( k \) | = | \( 21 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(8))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 43 | 21 | 22 |
Cusp forms | 37 | 19 | 18 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
8.21.c | \(\chi_{8}(7, \cdot)\) | None | 0 | 1 |
8.21.d | \(\chi_{8}(3, \cdot)\) | 8.21.d.a | 1 | 1 |
8.21.d.b | 18 |
Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces
\( S_{21}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 1}\)