Defining parameters
| Level: | \( N \) | = | \( 392 = 2^{3} \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(9408\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(392))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 379 | 108 | 271 |
| Cusp forms | 19 | 11 | 8 |
| Eisenstein series | 360 | 97 | 263 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 11 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(392))\)
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 the newforms together with their dimension.
| Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
|---|---|---|---|---|
| 392.1.c | \(\chi_{392}(97, \cdot)\) | None | 0 | 1 |
| 392.1.d | \(\chi_{392}(295, \cdot)\) | None | 0 | 1 |
| 392.1.g | \(\chi_{392}(99, \cdot)\) | 392.1.g.a | 1 | 1 |
| 392.1.g.b | 2 | |||
| 392.1.h | \(\chi_{392}(293, \cdot)\) | None | 0 | 1 |
| 392.1.j | \(\chi_{392}(117, \cdot)\) | 392.1.j.a | 2 | 2 |
| 392.1.k | \(\chi_{392}(67, \cdot)\) | 392.1.k.a | 2 | 2 |
| 392.1.k.b | 4 | |||
| 392.1.n | \(\chi_{392}(79, \cdot)\) | None | 0 | 2 |
| 392.1.o | \(\chi_{392}(129, \cdot)\) | None | 0 | 2 |
| 392.1.r | \(\chi_{392}(13, \cdot)\) | None | 0 | 6 |
| 392.1.s | \(\chi_{392}(43, \cdot)\) | None | 0 | 6 |
| 392.1.v | \(\chi_{392}(15, \cdot)\) | None | 0 | 6 |
| 392.1.w | \(\chi_{392}(41, \cdot)\) | None | 0 | 6 |
| 392.1.ba | \(\chi_{392}(17, \cdot)\) | None | 0 | 12 |
| 392.1.bb | \(\chi_{392}(23, \cdot)\) | None | 0 | 12 |
| 392.1.be | \(\chi_{392}(11, \cdot)\) | None | 0 | 12 |
| 392.1.bf | \(\chi_{392}(5, \cdot)\) | None | 0 | 12 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(392))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(392)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)