Defining parameters
| Level: | \( N \) | = | \( 5041 = 71^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(4234440\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5041))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1062320 | 1061830 | 490 |
| Cusp forms | 1054901 | 1054549 | 352 |
| Eisenstein series | 7419 | 7281 | 138 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5041))\)
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 |
|---|---|---|---|---|
| 5041.2.a | \(\chi_{5041}(1, \cdot)\) | 5041.2.a.a | 3 | 1 |
| 5041.2.a.b | 3 | |||
| 5041.2.a.c | 4 | |||
| 5041.2.a.d | 6 | |||
| 5041.2.a.e | 6 | |||
| 5041.2.a.f | 7 | |||
| 5041.2.a.g | 7 | |||
| 5041.2.a.h | 7 | |||
| 5041.2.a.i | 10 | |||
| 5041.2.a.j | 10 | |||
| 5041.2.a.k | 14 | |||
| 5041.2.a.l | 15 | |||
| 5041.2.a.m | 15 | |||
| 5041.2.a.n | 18 | |||
| 5041.2.a.o | 18 | |||
| 5041.2.a.p | 20 | |||
| 5041.2.a.q | 36 | |||
| 5041.2.a.r | 60 | |||
| 5041.2.a.s | 60 | |||
| 5041.2.a.t | 60 | |||
| 5041.2.c | \(\chi_{5041}(1335, \cdot)\) | n/a | 1520 | 4 |
| 5041.2.d | \(\chi_{5041}(261, \cdot)\) | n/a | 2280 | 6 |
| 5041.2.g | \(\chi_{5041}(121, \cdot)\) | n/a | 9120 | 24 |
| 5041.2.i | \(\chi_{5041}(72, \cdot)\) | n/a | 29750 | 70 |
| 5041.2.k | \(\chi_{5041}(5, \cdot)\) | n/a | 119000 | 280 |
| 5041.2.l | \(\chi_{5041}(20, \cdot)\) | n/a | 178500 | 420 |
| 5041.2.o | \(\chi_{5041}(2, \cdot)\) | n/a | 714000 | 1680 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5041))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(5041)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 2}\)