Defining parameters
| Level: | \( N \) | = | \( 8048 = 2^{4} \cdot 503 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(8096256\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8048))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2031092 | 1140781 | 890311 |
| Cusp forms | 2017037 | 1136273 | 880764 |
| Eisenstein series | 14055 | 4508 | 9547 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8048))\)
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 |
|---|---|---|---|---|
| 8048.2.a | \(\chi_{8048}(1, \cdot)\) | 8048.2.a.a | 1 | 1 |
| 8048.2.a.b | 1 | |||
| 8048.2.a.c | 1 | |||
| 8048.2.a.d | 1 | |||
| 8048.2.a.e | 1 | |||
| 8048.2.a.f | 1 | |||
| 8048.2.a.g | 1 | |||
| 8048.2.a.h | 1 | |||
| 8048.2.a.i | 1 | |||
| 8048.2.a.j | 1 | |||
| 8048.2.a.k | 1 | |||
| 8048.2.a.l | 2 | |||
| 8048.2.a.m | 3 | |||
| 8048.2.a.n | 5 | |||
| 8048.2.a.o | 5 | |||
| 8048.2.a.p | 10 | |||
| 8048.2.a.q | 12 | |||
| 8048.2.a.r | 12 | |||
| 8048.2.a.s | 21 | |||
| 8048.2.a.t | 21 | |||
| 8048.2.a.u | 26 | |||
| 8048.2.a.v | 28 | |||
| 8048.2.a.w | 29 | |||
| 8048.2.a.x | 33 | |||
| 8048.2.a.y | 33 | |||
| 8048.2.b | \(\chi_{8048}(8047, \cdot)\) | n/a | 252 | 1 |
| 8048.2.c | \(\chi_{8048}(4025, \cdot)\) | None | 0 | 1 |
| 8048.2.h | \(\chi_{8048}(4023, \cdot)\) | None | 0 | 1 |
| 8048.2.j | \(\chi_{8048}(2013, \cdot)\) | n/a | 2008 | 2 |
| 8048.2.l | \(\chi_{8048}(2011, \cdot)\) | n/a | 2012 | 2 |
| 8048.2.m | \(\chi_{8048}(33, \cdot)\) | n/a | 62750 | 250 |
| 8048.2.n | \(\chi_{8048}(55, \cdot)\) | None | 0 | 250 |
| 8048.2.s | \(\chi_{8048}(9, \cdot)\) | None | 0 | 250 |
| 8048.2.t | \(\chi_{8048}(15, \cdot)\) | n/a | 63000 | 250 |
| 8048.2.u | \(\chi_{8048}(19, \cdot)\) | n/a | 503000 | 500 |
| 8048.2.w | \(\chi_{8048}(13, \cdot)\) | n/a | 503000 | 500 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8048))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(8048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4024))\)\(^{\oplus 2}\)