Defining parameters
| Level: | \( N \) | = | \( 1475 = 5^{2} \cdot 59 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Newform subspaces: | \( 9 \) | ||
| Sturm bound: | \(174000\) | ||
| Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1475))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1669 | 1201 | 468 |
| Cusp forms | 45 | 32 | 13 |
| Eisenstein series | 1624 | 1169 | 455 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 32 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1475))\)
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 |
|---|---|---|---|---|
| 1475.1.c | \(\chi_{1475}(176, \cdot)\) | 1475.1.c.a | 1 | 1 |
| 1475.1.c.b | 1 | |||
| 1475.1.c.c | 2 | |||
| 1475.1.c.d | 2 | |||
| 1475.1.d | \(\chi_{1475}(1474, \cdot)\) | 1475.1.d.a | 2 | 1 |
| 1475.1.f | \(\chi_{1475}(532, \cdot)\) | None | 0 | 2 |
| 1475.1.h | \(\chi_{1475}(294, \cdot)\) | 1475.1.h.a | 4 | 4 |
| 1475.1.h.b | 8 | |||
| 1475.1.i | \(\chi_{1475}(471, \cdot)\) | 1475.1.i.a | 4 | 4 |
| 1475.1.i.b | 8 | |||
| 1475.1.k | \(\chi_{1475}(178, \cdot)\) | None | 0 | 8 |
| 1475.1.n | \(\chi_{1475}(24, \cdot)\) | None | 0 | 28 |
| 1475.1.o | \(\chi_{1475}(101, \cdot)\) | None | 0 | 28 |
| 1475.1.q | \(\chi_{1475}(7, \cdot)\) | None | 0 | 56 |
| 1475.1.u | \(\chi_{1475}(6, \cdot)\) | None | 0 | 112 |
| 1475.1.v | \(\chi_{1475}(14, \cdot)\) | None | 0 | 112 |
| 1475.1.x | \(\chi_{1475}(3, \cdot)\) | None | 0 | 224 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1475))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1475)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(295))\)\(^{\oplus 2}\)