Defining parameters
| Level: | \( N \) | = | \( 16 = 2^{4} \) |
| Weight: | \( k \) | = | \( 3 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(48\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(16))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 23 | 11 | 12 |
| Cusp forms | 9 | 7 | 2 |
| Eisenstein series | 14 | 4 | 10 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)
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 |
|---|---|---|---|---|
| 16.3.c | \(\chi_{16}(15, \cdot)\) | 16.3.c.a | 1 | 1 |
| 16.3.d | \(\chi_{16}(7, \cdot)\) | None | 0 | 1 |
| 16.3.f | \(\chi_{16}(3, \cdot)\) | 16.3.f.a | 6 | 2 |
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)