Defining parameters
| Level: | \( N \) | = | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(35904\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(804))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 730 | 158 | 572 |
| Cusp forms | 70 | 26 | 44 |
| Eisenstein series | 660 | 132 | 528 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 26 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(804))\)
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 |
|---|---|---|---|---|
| 804.1.b | \(\chi_{804}(133, \cdot)\) | None | 0 | 1 |
| 804.1.d | \(\chi_{804}(269, \cdot)\) | None | 0 | 1 |
| 804.1.f | \(\chi_{804}(403, \cdot)\) | None | 0 | 1 |
| 804.1.h | \(\chi_{804}(803, \cdot)\) | 804.1.h.a | 1 | 1 |
| 804.1.h.b | 1 | |||
| 804.1.h.c | 1 | |||
| 804.1.h.d | 1 | |||
| 804.1.k | \(\chi_{804}(29, \cdot)\) | 804.1.k.a | 2 | 2 |
| 804.1.m | \(\chi_{804}(97, \cdot)\) | None | 0 | 2 |
| 804.1.n | \(\chi_{804}(239, \cdot)\) | None | 0 | 2 |
| 804.1.p | \(\chi_{804}(163, \cdot)\) | None | 0 | 2 |
| 804.1.r | \(\chi_{804}(119, \cdot)\) | None | 0 | 10 |
| 804.1.t | \(\chi_{804}(91, \cdot)\) | None | 0 | 10 |
| 804.1.v | \(\chi_{804}(89, \cdot)\) | None | 0 | 10 |
| 804.1.x | \(\chi_{804}(109, \cdot)\) | None | 0 | 10 |
| 804.1.z | \(\chi_{804}(19, \cdot)\) | None | 0 | 20 |
| 804.1.bb | \(\chi_{804}(11, \cdot)\) | None | 0 | 20 |
| 804.1.bc | \(\chi_{804}(13, \cdot)\) | None | 0 | 20 |
| 804.1.be | \(\chi_{804}(17, \cdot)\) | 804.1.be.a | 20 | 20 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(804))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(804)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(201))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(268))\)\(^{\oplus 2}\)