Defining parameters
| Level: | \( N \) | = | \( 10002 = 2 \cdot 3 \cdot 1667 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 12 \) | ||
| Sturm bound: | \(11115552\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10002))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 2785552 | 694723 | 2090829 |
| Cusp forms | 2772225 | 694723 | 2077502 |
| Eisenstein series | 13327 | 0 | 13327 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10002))\)
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 |
|---|---|---|---|---|
| 10002.2.a | \(\chi_{10002}(1, \cdot)\) | 10002.2.a.a | 1 | 1 |
| 10002.2.a.b | 1 | |||
| 10002.2.a.c | 1 | |||
| 10002.2.a.d | 1 | |||
| 10002.2.a.e | 1 | |||
| 10002.2.a.f | 3 | |||
| 10002.2.a.g | 19 | |||
| 10002.2.a.h | 28 | |||
| 10002.2.a.i | 29 | |||
| 10002.2.a.j | 32 | |||
| 10002.2.a.k | 38 | |||
| 10002.2.a.l | 38 | |||
| 10002.2.a.m | 40 | |||
| 10002.2.a.n | 47 | |||
| 10002.2.d | \(\chi_{10002}(10001, \cdot)\) | n/a | 556 | 1 |
| 10002.2.e | \(\chi_{10002}(1843, \cdot)\) | n/a | 1668 | 6 |
| 10002.2.f | \(\chi_{10002}(3047, \cdot)\) | n/a | 3336 | 6 |
| 10002.2.i | \(\chi_{10002}(415, \cdot)\) | n/a | 4448 | 16 |
| 10002.2.j | \(\chi_{10002}(263, \cdot)\) | n/a | 8896 | 16 |
| 10002.2.m | \(\chi_{10002}(13, \cdot)\) | n/a | 11676 | 42 |
| 10002.2.o | \(\chi_{10002}(179, \cdot)\) | n/a | 23352 | 42 |
| 10002.2.q | \(\chi_{10002}(307, \cdot)\) | n/a | 26688 | 96 |
| 10002.2.t | \(\chi_{10002}(59, \cdot)\) | n/a | 53376 | 96 |
| 10002.2.u | \(\chi_{10002}(19, \cdot)\) | n/a | 186816 | 672 |
| 10002.2.w | \(\chi_{10002}(5, \cdot)\) | n/a | 373632 | 672 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(10002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1667))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3334))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5001))\)\(^{\oplus 2}\)