Defining parameters
| Level: | \( N \) | = | \( 148 = 2^{2} \cdot 37 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 3 \) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(1368\) | ||
| Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(148))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 100 | 44 | 56 |
| Cusp forms | 10 | 10 | 0 |
| Eisenstein series | 90 | 34 | 56 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 2 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)
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 |
|---|---|---|---|---|
| 148.1.b | \(\chi_{148}(147, \cdot)\) | None | 0 | 1 |
| 148.1.c | \(\chi_{148}(75, \cdot)\) | None | 0 | 1 |
| 148.1.f | \(\chi_{148}(105, \cdot)\) | 148.1.f.a | 2 | 2 |
| 148.1.i | \(\chi_{148}(47, \cdot)\) | 148.1.i.a | 2 | 2 |
| 148.1.j | \(\chi_{148}(11, \cdot)\) | None | 0 | 2 |
| 148.1.m | \(\chi_{148}(29, \cdot)\) | None | 0 | 4 |
| 148.1.o | \(\chi_{148}(3, \cdot)\) | None | 0 | 6 |
| 148.1.p | \(\chi_{148}(7, \cdot)\) | 148.1.p.a | 6 | 6 |
| 148.1.r | \(\chi_{148}(5, \cdot)\) | None | 0 | 12 |