Defining parameters
| Level: | \( N \) | = | \( 50 = 2 \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 22 \) |
| Nonzero newspaces: | \( 4 \) | ||
| Sturm bound: | \(3300\) | ||
| Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(50))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1603 | 485 | 1118 |
| Cusp forms | 1547 | 485 | 1062 |
| Eisenstein series | 56 | 0 | 56 |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(50))\)
We only show spaces with even 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 |
|---|---|---|---|---|
| 50.22.a | \(\chi_{50}(1, \cdot)\) | 50.22.a.a | 1 | 1 |
| 50.22.a.b | 1 | |||
| 50.22.a.c | 1 | |||
| 50.22.a.d | 2 | |||
| 50.22.a.e | 2 | |||
| 50.22.a.f | 2 | |||
| 50.22.a.g | 3 | |||
| 50.22.a.h | 3 | |||
| 50.22.a.i | 4 | |||
| 50.22.a.j | 4 | |||
| 50.22.a.k | 5 | |||
| 50.22.a.l | 5 | |||
| 50.22.b | \(\chi_{50}(49, \cdot)\) | 50.22.b.a | 2 | 1 |
| 50.22.b.b | 2 | |||
| 50.22.b.c | 2 | |||
| 50.22.b.d | 4 | |||
| 50.22.b.e | 4 | |||
| 50.22.b.f | 4 | |||
| 50.22.b.g | 6 | |||
| 50.22.b.h | 8 | |||
| 50.22.d | \(\chi_{50}(11, \cdot)\) | n/a | 212 | 4 |
| 50.22.e | \(\chi_{50}(9, \cdot)\) | n/a | 208 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)