Defining parameters
| Level: | \( N \) | = | \( 4024 = 2^{3} \cdot 503 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 6 \) | ||
| Sturm bound: | \(2024064\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4024))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 509028 | 285634 | 223394 |
| Cusp forms | 503005 | 283630 | 219375 |
| Eisenstein series | 6023 | 2004 | 4019 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4024))\)
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 |
|---|---|---|---|---|
| 4024.2.a | \(\chi_{4024}(1, \cdot)\) | 4024.2.a.a | 1 | 1 |
| 4024.2.a.b | 1 | |||
| 4024.2.a.c | 1 | |||
| 4024.2.a.d | 28 | |||
| 4024.2.a.e | 29 | |||
| 4024.2.a.f | 33 | |||
| 4024.2.a.g | 33 | |||
| 4024.2.b | \(\chi_{4024}(4023, \cdot)\) | None | 0 | 1 |
| 4024.2.c | \(\chi_{4024}(2013, \cdot)\) | n/a | 502 | 1 |
| 4024.2.h | \(\chi_{4024}(2011, \cdot)\) | n/a | 502 | 1 |
| 4024.2.i | \(\chi_{4024}(9, \cdot)\) | n/a | 31500 | 250 |
| 4024.2.j | \(\chi_{4024}(19, \cdot)\) | n/a | 125500 | 250 |
| 4024.2.o | \(\chi_{4024}(13, \cdot)\) | n/a | 125500 | 250 |
| 4024.2.p | \(\chi_{4024}(15, \cdot)\) | None | 0 | 250 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4024))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 2}\)