Defining parameters
| Level: | \( N \) | = | \( 669 = 3 \cdot 223 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Newform subspaces: | \( 23 \) | ||
| Sturm bound: | \(66304\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(669))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 17020 | 12653 | 4367 |
| Cusp forms | 16133 | 12209 | 3924 |
| Eisenstein series | 887 | 444 | 443 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)
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 |
|---|---|---|---|---|
| 669.2.a | \(\chi_{669}(1, \cdot)\) | 669.2.a.a | 1 | 1 |
| 669.2.a.b | 2 | |||
| 669.2.a.c | 2 | |||
| 669.2.a.d | 2 | |||
| 669.2.a.e | 3 | |||
| 669.2.a.f | 3 | |||
| 669.2.a.g | 3 | |||
| 669.2.a.h | 7 | |||
| 669.2.a.i | 14 | |||
| 669.2.c | \(\chi_{669}(668, \cdot)\) | 669.2.c.a | 72 | 1 |
| 669.2.e | \(\chi_{669}(262, \cdot)\) | 669.2.e.a | 2 | 2 |
| 669.2.e.b | 4 | |||
| 669.2.e.c | 30 | |||
| 669.2.e.d | 38 | |||
| 669.2.f | \(\chi_{669}(263, \cdot)\) | 669.2.f.a | 2 | 2 |
| 669.2.f.b | 144 | |||
| 669.2.i | \(\chi_{669}(4, \cdot)\) | 669.2.i.a | 648 | 36 |
| 669.2.i.b | 720 | |||
| 669.2.k | \(\chi_{669}(26, \cdot)\) | 669.2.k.a | 2592 | 36 |
| 669.2.m | \(\chi_{669}(19, \cdot)\) | 669.2.m.a | 1296 | 72 |
| 669.2.m.b | 1368 | |||
| 669.2.p | \(\chi_{669}(5, \cdot)\) | 669.2.p.a | 72 | 72 |
| 669.2.p.b | 5184 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(669))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(669)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 2}\)