Defining parameters
| Level: | \( N \) | = | \( 444 = 2^{2} \cdot 3 \cdot 37 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(10944\) | ||
| Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(444))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 415 | 86 | 329 |
| Cusp forms | 55 | 14 | 41 |
| Eisenstein series | 360 | 72 | 288 |
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 \(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)
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 |
|---|---|---|---|---|
| 444.1.b | \(\chi_{444}(295, \cdot)\) | None | 0 | 1 |
| 444.1.d | \(\chi_{444}(149, \cdot)\) | None | 0 | 1 |
| 444.1.f | \(\chi_{444}(223, \cdot)\) | None | 0 | 1 |
| 444.1.h | \(\chi_{444}(221, \cdot)\) | 444.1.h.a | 2 | 1 |
| 444.1.j | \(\chi_{444}(179, \cdot)\) | None | 0 | 2 |
| 444.1.l | \(\chi_{444}(253, \cdot)\) | None | 0 | 2 |
| 444.1.n | \(\chi_{444}(101, \cdot)\) | None | 0 | 2 |
| 444.1.o | \(\chi_{444}(211, \cdot)\) | None | 0 | 2 |
| 444.1.q | \(\chi_{444}(137, \cdot)\) | None | 0 | 2 |
| 444.1.s | \(\chi_{444}(175, \cdot)\) | None | 0 | 2 |
| 444.1.v | \(\chi_{444}(97, \cdot)\) | None | 0 | 4 |
| 444.1.x | \(\chi_{444}(23, \cdot)\) | None | 0 | 4 |
| 444.1.bc | \(\chi_{444}(41, \cdot)\) | 444.1.bc.a | 6 | 6 |
| 444.1.bd | \(\chi_{444}(67, \cdot)\) | None | 0 | 6 |
| 444.1.be | \(\chi_{444}(7, \cdot)\) | None | 0 | 6 |
| 444.1.bf | \(\chi_{444}(53, \cdot)\) | 444.1.bf.a | 6 | 6 |
| 444.1.bi | \(\chi_{444}(35, \cdot)\) | None | 0 | 12 |
| 444.1.bj | \(\chi_{444}(13, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(444))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(444)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)