Defining parameters
| Level: | \( N \) | = | \( 448 = 2^{6} \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(12288\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(448))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 474 | 124 | 350 |
| Cusp forms | 42 | 14 | 28 |
| Eisenstein series | 432 | 110 | 322 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 10 | 4 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)
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 |
|---|---|---|---|---|
| 448.1.c | \(\chi_{448}(321, \cdot)\) | None | 0 | 1 |
| 448.1.d | \(\chi_{448}(127, \cdot)\) | None | 0 | 1 |
| 448.1.g | \(\chi_{448}(351, \cdot)\) | None | 0 | 1 |
| 448.1.h | \(\chi_{448}(97, \cdot)\) | None | 0 | 1 |
| 448.1.k | \(\chi_{448}(15, \cdot)\) | None | 0 | 2 |
| 448.1.l | \(\chi_{448}(209, \cdot)\) | 448.1.l.a | 2 | 2 |
| 448.1.n | \(\chi_{448}(33, \cdot)\) | None | 0 | 2 |
| 448.1.o | \(\chi_{448}(95, \cdot)\) | None | 0 | 2 |
| 448.1.r | \(\chi_{448}(191, \cdot)\) | 448.1.r.a | 4 | 2 |
| 448.1.s | \(\chi_{448}(129, \cdot)\) | None | 0 | 2 |
| 448.1.v | \(\chi_{448}(41, \cdot)\) | None | 0 | 4 |
| 448.1.w | \(\chi_{448}(71, \cdot)\) | None | 0 | 4 |
| 448.1.y | \(\chi_{448}(79, \cdot)\) | None | 0 | 4 |
| 448.1.bb | \(\chi_{448}(17, \cdot)\) | None | 0 | 4 |
| 448.1.be | \(\chi_{448}(43, \cdot)\) | None | 0 | 8 |
| 448.1.bf | \(\chi_{448}(13, \cdot)\) | 448.1.bf.a | 8 | 8 |
| 448.1.bg | \(\chi_{448}(73, \cdot)\) | None | 0 | 8 |
| 448.1.bj | \(\chi_{448}(23, \cdot)\) | None | 0 | 8 |
| 448.1.bk | \(\chi_{448}(5, \cdot)\) | None | 0 | 16 |
| 448.1.bl | \(\chi_{448}(11, \cdot)\) | None | 0 | 16 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(448)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 1}\)