Defining parameters
| Level: | \( N \) | = | \( 441 = 3^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(14112\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(441))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 508 | 232 | 276 |
| Cusp forms | 28 | 14 | 14 |
| Eisenstein series | 480 | 218 | 262 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 14 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(441))\)
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 |
|---|---|---|---|---|
| 441.1.b | \(\chi_{441}(197, \cdot)\) | 441.1.b.a | 2 | 1 |
| 441.1.d | \(\chi_{441}(244, \cdot)\) | None | 0 | 1 |
| 441.1.j | \(\chi_{441}(263, \cdot)\) | None | 0 | 2 |
| 441.1.k | \(\chi_{441}(31, \cdot)\) | None | 0 | 2 |
| 441.1.l | \(\chi_{441}(97, \cdot)\) | None | 0 | 2 |
| 441.1.m | \(\chi_{441}(19, \cdot)\) | 441.1.m.a | 2 | 2 |
| 441.1.n | \(\chi_{441}(128, \cdot)\) | None | 0 | 2 |
| 441.1.q | \(\chi_{441}(116, \cdot)\) | 441.1.q.a | 4 | 2 |
| 441.1.r | \(\chi_{441}(50, \cdot)\) | None | 0 | 2 |
| 441.1.t | \(\chi_{441}(166, \cdot)\) | None | 0 | 2 |
| 441.1.v | \(\chi_{441}(55, \cdot)\) | 441.1.v.a | 6 | 6 |
| 441.1.x | \(\chi_{441}(8, \cdot)\) | None | 0 | 6 |
| 441.1.bc | \(\chi_{441}(40, \cdot)\) | None | 0 | 12 |
| 441.1.be | \(\chi_{441}(29, \cdot)\) | None | 0 | 12 |
| 441.1.bf | \(\chi_{441}(44, \cdot)\) | None | 0 | 12 |
| 441.1.bi | \(\chi_{441}(2, \cdot)\) | None | 0 | 12 |
| 441.1.bj | \(\chi_{441}(10, \cdot)\) | None | 0 | 12 |
| 441.1.bk | \(\chi_{441}(13, \cdot)\) | None | 0 | 12 |
| 441.1.bl | \(\chi_{441}(61, \cdot)\) | None | 0 | 12 |
| 441.1.bm | \(\chi_{441}(11, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)