Defining parameters
| Level: | \( N \) | = | \( 6023 = 19 \cdot 317 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 18 \) | ||
| Sturm bound: | \(6029280\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6023))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1513008 | 1504271 | 8737 |
| Cusp forms | 1501633 | 1493559 | 8074 |
| Eisenstein series | 11375 | 10712 | 663 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6023))\)
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 |
|---|---|---|---|---|
| 6023.2.a | \(\chi_{6023}(1, \cdot)\) | 6023.2.a.a | 98 | 1 |
| 6023.2.a.b | 99 | |||
| 6023.2.a.c | 138 | |||
| 6023.2.a.d | 140 | |||
| 6023.2.b | \(\chi_{6023}(1901, \cdot)\) | n/a | 476 | 1 |
| 6023.2.e | \(\chi_{6023}(3488, \cdot)\) | n/a | 1056 | 2 |
| 6023.2.f | \(\chi_{6023}(4958, \cdot)\) | n/a | 1056 | 2 |
| 6023.2.j | \(\chi_{6023}(1584, \cdot)\) | n/a | 1056 | 2 |
| 6023.2.k | \(\chi_{6023}(1586, \cdot)\) | n/a | 3156 | 6 |
| 6023.2.m | \(\chi_{6023}(1471, \cdot)\) | n/a | 2112 | 4 |
| 6023.2.o | \(\chi_{6023}(633, \cdot)\) | n/a | 3168 | 6 |
| 6023.2.r | \(\chi_{6023}(203, \cdot)\) | n/a | 6336 | 12 |
| 6023.2.s | \(\chi_{6023}(438, \cdot)\) | n/a | 37284 | 78 |
| 6023.2.v | \(\chi_{6023}(39, \cdot)\) | n/a | 37128 | 78 |
| 6023.2.w | \(\chi_{6023}(11, \cdot)\) | n/a | 82368 | 156 |
| 6023.2.y | \(\chi_{6023}(18, \cdot)\) | n/a | 82368 | 156 |
| 6023.2.z | \(\chi_{6023}(7, \cdot)\) | n/a | 82368 | 156 |
| 6023.2.bc | \(\chi_{6023}(16, \cdot)\) | n/a | 247104 | 468 |
| 6023.2.bd | \(\chi_{6023}(8, \cdot)\) | n/a | 164736 | 312 |
| 6023.2.bg | \(\chi_{6023}(4, \cdot)\) | n/a | 247104 | 468 |
| 6023.2.bi | \(\chi_{6023}(2, \cdot)\) | n/a | 494208 | 936 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6023))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(317))\)\(^{\oplus 2}\)