Defining parameters
| Level: | \( N \) | = | \( 344 = 2^{3} \cdot 43 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(7392\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(344))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 284 | 112 | 172 |
| Cusp forms | 32 | 30 | 2 |
| Eisenstein series | 252 | 82 | 170 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 24 | 4 | 2 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(344))\)
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 |
|---|---|---|---|---|
| 344.1.b | \(\chi_{344}(257, \cdot)\) | 344.1.b.a | 2 | 1 |
| 344.1.d | \(\chi_{344}(87, \cdot)\) | None | 0 | 1 |
| 344.1.f | \(\chi_{344}(259, \cdot)\) | None | 0 | 1 |
| 344.1.h | \(\chi_{344}(85, \cdot)\) | 344.1.h.a | 2 | 1 |
| 344.1.h.b | 2 | |||
| 344.1.j | \(\chi_{344}(37, \cdot)\) | None | 0 | 2 |
| 344.1.l | \(\chi_{344}(251, \cdot)\) | 344.1.l.a | 2 | 2 |
| 344.1.l.b | 4 | |||
| 344.1.n | \(\chi_{344}(79, \cdot)\) | None | 0 | 2 |
| 344.1.p | \(\chi_{344}(209, \cdot)\) | None | 0 | 2 |
| 344.1.r | \(\chi_{344}(45, \cdot)\) | None | 0 | 6 |
| 344.1.s | \(\chi_{344}(11, \cdot)\) | 344.1.s.a | 6 | 6 |
| 344.1.u | \(\chi_{344}(47, \cdot)\) | None | 0 | 6 |
| 344.1.w | \(\chi_{344}(65, \cdot)\) | None | 0 | 6 |
| 344.1.ba | \(\chi_{344}(33, \cdot)\) | None | 0 | 12 |
| 344.1.bc | \(\chi_{344}(15, \cdot)\) | None | 0 | 12 |
| 344.1.be | \(\chi_{344}(67, \cdot)\) | 344.1.be.a | 12 | 12 |
| 344.1.bf | \(\chi_{344}(5, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(344))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(344)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(86))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(172))\)\(^{\oplus 2}\)