Defining parameters
| Level: | \( N \) | = | \( 4842 = 2 \cdot 3^{2} \cdot 269 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(2604960\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4842))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 655528 | 171851 | 483677 |
| Cusp forms | 646953 | 171851 | 475102 |
| Eisenstein series | 8575 | 0 | 8575 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4842))\)
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 |
|---|---|---|---|---|
| 4842.2.a | \(\chi_{4842}(1, \cdot)\) | 4842.2.a.a | 1 | 1 |
| 4842.2.a.b | 1 | |||
| 4842.2.a.c | 1 | |||
| 4842.2.a.d | 2 | |||
| 4842.2.a.e | 2 | |||
| 4842.2.a.f | 2 | |||
| 4842.2.a.g | 3 | |||
| 4842.2.a.h | 3 | |||
| 4842.2.a.i | 3 | |||
| 4842.2.a.j | 4 | |||
| 4842.2.a.k | 5 | |||
| 4842.2.a.l | 6 | |||
| 4842.2.a.m | 6 | |||
| 4842.2.a.n | 7 | |||
| 4842.2.a.o | 7 | |||
| 4842.2.a.p | 8 | |||
| 4842.2.a.q | 8 | |||
| 4842.2.a.r | 9 | |||
| 4842.2.a.s | 9 | |||
| 4842.2.a.t | 13 | |||
| 4842.2.a.u | 13 | |||
| 4842.2.d | \(\chi_{4842}(4303, \cdot)\) | n/a | 112 | 1 |
| 4842.2.e | \(\chi_{4842}(1615, \cdot)\) | n/a | 536 | 2 |
| 4842.2.f | \(\chi_{4842}(2339, \cdot)\) | n/a | 180 | 2 |
| 4842.2.h | \(\chi_{4842}(1075, \cdot)\) | n/a | 540 | 2 |
| 4842.2.l | \(\chi_{4842}(725, \cdot)\) | n/a | 1080 | 4 |
| 4842.2.m | \(\chi_{4842}(37, \cdot)\) | n/a | 7458 | 66 |
| 4842.2.n | \(\chi_{4842}(55, \cdot)\) | n/a | 7392 | 66 |
| 4842.2.q | \(\chi_{4842}(25, \cdot)\) | n/a | 35640 | 132 |
| 4842.2.s | \(\chi_{4842}(17, \cdot)\) | n/a | 11880 | 132 |
| 4842.2.v | \(\chi_{4842}(13, \cdot)\) | n/a | 35640 | 132 |
| 4842.2.w | \(\chi_{4842}(29, \cdot)\) | n/a | 71280 | 264 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4842))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4842)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(269))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(538))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(807))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1614))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2421))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4842))\)\(^{\oplus 1}\)