Defining parameters
| Level: | \( N \) | = | \( 147 = 3 \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(1568\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(147))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 126 | 55 | 71 |
| Cusp forms | 6 | 6 | 0 |
| Eisenstein series | 120 | 49 | 71 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)
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 |
|---|---|---|---|---|
| 147.1.b | \(\chi_{147}(50, \cdot)\) | None | 0 | 1 |
| 147.1.d | \(\chi_{147}(97, \cdot)\) | None | 0 | 1 |
| 147.1.f | \(\chi_{147}(19, \cdot)\) | None | 0 | 2 |
| 147.1.h | \(\chi_{147}(116, \cdot)\) | None | 0 | 2 |
| 147.1.j | \(\chi_{147}(13, \cdot)\) | None | 0 | 6 |
| 147.1.l | \(\chi_{147}(8, \cdot)\) | 147.1.l.a | 6 | 6 |
| 147.1.n | \(\chi_{147}(2, \cdot)\) | None | 0 | 12 |
| 147.1.p | \(\chi_{147}(10, \cdot)\) | None | 0 | 12 |