Defining parameters
| Level: | \( N \) | = | \( 308 = 2^{2} \cdot 7 \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(5760\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(308))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 324 | 102 | 222 |
| Cusp forms | 24 | 10 | 14 |
| Eisenstein series | 300 | 92 | 208 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(308))\)
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 |
|---|---|---|---|---|
| 308.1.b | \(\chi_{308}(265, \cdot)\) | None | 0 | 1 |
| 308.1.e | \(\chi_{308}(155, \cdot)\) | None | 0 | 1 |
| 308.1.g | \(\chi_{308}(307, \cdot)\) | 308.1.g.a | 1 | 1 |
| 308.1.g.b | 1 | |||
| 308.1.h | \(\chi_{308}(197, \cdot)\) | None | 0 | 1 |
| 308.1.k | \(\chi_{308}(65, \cdot)\) | None | 0 | 2 |
| 308.1.m | \(\chi_{308}(87, \cdot)\) | None | 0 | 2 |
| 308.1.o | \(\chi_{308}(23, \cdot)\) | None | 0 | 2 |
| 308.1.p | \(\chi_{308}(45, \cdot)\) | None | 0 | 2 |
| 308.1.r | \(\chi_{308}(29, \cdot)\) | None | 0 | 4 |
| 308.1.s | \(\chi_{308}(83, \cdot)\) | 308.1.s.a | 4 | 4 |
| 308.1.s.b | 4 | |||
| 308.1.u | \(\chi_{308}(15, \cdot)\) | None | 0 | 4 |
| 308.1.x | \(\chi_{308}(69, \cdot)\) | None | 0 | 4 |
| 308.1.ba | \(\chi_{308}(5, \cdot)\) | None | 0 | 8 |
| 308.1.bb | \(\chi_{308}(135, \cdot)\) | None | 0 | 8 |
| 308.1.bd | \(\chi_{308}(19, \cdot)\) | None | 0 | 8 |
| 308.1.bf | \(\chi_{308}(149, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(308))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(308)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(308))\)\(^{\oplus 1}\)