Defining parameters
| Level: | \( N \) | = | \( 921 = 3 \cdot 307 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(62832\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(921))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 668 | 358 | 310 |
| Cusp forms | 56 | 54 | 2 |
| Eisenstein series | 612 | 304 | 308 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 50 | 0 | 4 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(921))\)
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 |
|---|---|---|---|---|
| 921.1.b | \(\chi_{921}(308, \cdot)\) | None | 0 | 1 |
| 921.1.c | \(\chi_{921}(613, \cdot)\) | None | 0 | 1 |
| 921.1.f | \(\chi_{921}(325, \cdot)\) | None | 0 | 2 |
| 921.1.g | \(\chi_{921}(17, \cdot)\) | 921.1.g.a | 2 | 2 |
| 921.1.g.b | 4 | |||
| 921.1.l | \(\chi_{921}(139, \cdot)\) | None | 0 | 6 |
| 921.1.m | \(\chi_{921}(53, \cdot)\) | None | 0 | 6 |
| 921.1.o | \(\chi_{921}(34, \cdot)\) | None | 0 | 16 |
| 921.1.p | \(\chi_{921}(269, \cdot)\) | 921.1.p.a | 16 | 16 |
| 921.1.s | \(\chi_{921}(68, \cdot)\) | 921.1.s.a | 32 | 32 |
| 921.1.t | \(\chi_{921}(136, \cdot)\) | None | 0 | 32 |
| 921.1.v | \(\chi_{921}(13, \cdot)\) | None | 0 | 96 |
| 921.1.w | \(\chi_{921}(11, \cdot)\) | None | 0 | 96 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(921))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(921)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(307))\)\(^{\oplus 2}\)