Defining parameters
| Level: | \( N \) | = | \( 196 = 2^{2} \cdot 7^{2} \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 2 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(2352\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(196))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 153 | 52 | 101 |
| Cusp forms | 3 | 3 | 0 |
| Eisenstein series | 150 | 49 | 101 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)
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 |
|---|---|---|---|---|
| 196.1.b | \(\chi_{196}(97, \cdot)\) | None | 0 | 1 |
| 196.1.c | \(\chi_{196}(99, \cdot)\) | 196.1.c.a | 1 | 1 |
| 196.1.g | \(\chi_{196}(67, \cdot)\) | 196.1.g.a | 2 | 2 |
| 196.1.h | \(\chi_{196}(117, \cdot)\) | None | 0 | 2 |
| 196.1.k | \(\chi_{196}(15, \cdot)\) | None | 0 | 6 |
| 196.1.l | \(\chi_{196}(13, \cdot)\) | None | 0 | 6 |
| 196.1.n | \(\chi_{196}(5, \cdot)\) | None | 0 | 12 |
| 196.1.o | \(\chi_{196}(11, \cdot)\) | None | 0 | 12 |