Defining parameters
| Level: | \( N \) | = | \( 1805 = 5 \cdot 19^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 5 \) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(259920\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1805))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2064 | 1448 | 616 |
| Cusp forms | 48 | 42 | 6 |
| Eisenstein series | 2016 | 1406 | 610 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 42 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1805))\)
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 |
|---|---|---|---|---|
| 1805.1.c | \(\chi_{1805}(721, \cdot)\) | None | 0 | 1 |
| 1805.1.d | \(\chi_{1805}(1804, \cdot)\) | None | 0 | 1 |
| 1805.1.f | \(\chi_{1805}(362, \cdot)\) | 1805.1.f.a | 2 | 2 |
| 1805.1.h | \(\chi_{1805}(69, \cdot)\) | 1805.1.h.a | 2 | 2 |
| 1805.1.h.b | 4 | |||
| 1805.1.j | \(\chi_{1805}(791, \cdot)\) | None | 0 | 2 |
| 1805.1.m | \(\chi_{1805}(68, \cdot)\) | 1805.1.m.a | 4 | 4 |
| 1805.1.n | \(\chi_{1805}(116, \cdot)\) | None | 0 | 6 |
| 1805.1.o | \(\chi_{1805}(299, \cdot)\) | 1805.1.o.a | 6 | 6 |
| 1805.1.o.b | 12 | |||
| 1805.1.r | \(\chi_{1805}(28, \cdot)\) | 1805.1.r.a | 12 | 12 |
| 1805.1.t | \(\chi_{1805}(94, \cdot)\) | None | 0 | 18 |
| 1805.1.u | \(\chi_{1805}(56, \cdot)\) | None | 0 | 18 |
| 1805.1.y | \(\chi_{1805}(58, \cdot)\) | None | 0 | 36 |
| 1805.1.z | \(\chi_{1805}(31, \cdot)\) | None | 0 | 36 |
| 1805.1.bb | \(\chi_{1805}(84, \cdot)\) | None | 0 | 36 |
| 1805.1.bd | \(\chi_{1805}(7, \cdot)\) | None | 0 | 72 |
| 1805.1.bg | \(\chi_{1805}(14, \cdot)\) | None | 0 | 108 |
| 1805.1.bh | \(\chi_{1805}(21, \cdot)\) | None | 0 | 108 |
| 1805.1.bj | \(\chi_{1805}(17, \cdot)\) | None | 0 | 216 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1805))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1805)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)