Defining parameters
| Level: | \( N \) | = | \( 152 = 2^{3} \cdot 19 \) |
| Weight: | \( k \) | = | \( 16 \) |
| Nonzero newspaces: | \( 9 \) | ||
| Sturm bound: | \(23040\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(152))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 10908 | 6071 | 4837 |
| Cusp forms | 10692 | 6003 | 4689 |
| Eisenstein series | 216 | 68 | 148 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(152))\)
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 |
|---|---|---|---|---|
| 152.16.a | \(\chi_{152}(1, \cdot)\) | 152.16.a.a | 15 | 1 |
| 152.16.a.b | 17 | |||
| 152.16.a.c | 17 | |||
| 152.16.a.d | 18 | |||
| 152.16.b | \(\chi_{152}(75, \cdot)\) | n/a | 298 | 1 |
| 152.16.c | \(\chi_{152}(77, \cdot)\) | n/a | 270 | 1 |
| 152.16.h | \(\chi_{152}(151, \cdot)\) | None | 0 | 1 |
| 152.16.i | \(\chi_{152}(49, \cdot)\) | n/a | 150 | 2 |
| 152.16.j | \(\chi_{152}(31, \cdot)\) | None | 0 | 2 |
| 152.16.o | \(\chi_{152}(27, \cdot)\) | n/a | 596 | 2 |
| 152.16.p | \(\chi_{152}(45, \cdot)\) | n/a | 596 | 2 |
| 152.16.q | \(\chi_{152}(9, \cdot)\) | n/a | 450 | 6 |
| 152.16.t | \(\chi_{152}(5, \cdot)\) | n/a | 1788 | 6 |
| 152.16.v | \(\chi_{152}(3, \cdot)\) | n/a | 1788 | 6 |
| 152.16.w | \(\chi_{152}(15, \cdot)\) | None | 0 | 6 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(152)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)