Defining parameters
| Level: | \( N \) | = | \( 395 = 5 \cdot 79 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(12480\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(395))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 323 | 237 | 86 |
| Cusp forms | 11 | 7 | 4 |
| Eisenstein series | 312 | 230 | 82 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 7 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(395))\)
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 |
|---|---|---|---|---|
| 395.1.c | \(\chi_{395}(394, \cdot)\) | 395.1.c.a | 1 | 1 |
| 395.1.c.b | 2 | |||
| 395.1.c.c | 4 | |||
| 395.1.d | \(\chi_{395}(236, \cdot)\) | None | 0 | 1 |
| 395.1.g | \(\chi_{395}(238, \cdot)\) | None | 0 | 2 |
| 395.1.h | \(\chi_{395}(56, \cdot)\) | None | 0 | 2 |
| 395.1.i | \(\chi_{395}(24, \cdot)\) | None | 0 | 2 |
| 395.1.k | \(\chi_{395}(23, \cdot)\) | None | 0 | 4 |
| 395.1.n | \(\chi_{395}(41, \cdot)\) | None | 0 | 12 |
| 395.1.o | \(\chi_{395}(14, \cdot)\) | None | 0 | 12 |
| 395.1.r | \(\chi_{395}(8, \cdot)\) | None | 0 | 24 |
| 395.1.u | \(\chi_{395}(29, \cdot)\) | None | 0 | 24 |
| 395.1.v | \(\chi_{395}(6, \cdot)\) | None | 0 | 24 |
| 395.1.x | \(\chi_{395}(2, \cdot)\) | None | 0 | 48 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(395))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(395)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)