Defining parameters
Level: | \( N \) | = | \( 6378 = 2 \cdot 3 \cdot 1063 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(4519872\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6378))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1134216 | 282493 | 851723 |
Cusp forms | 1125721 | 282493 | 843228 |
Eisenstein series | 8495 | 0 | 8495 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6378))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
6378.2.a | \(\chi_{6378}(1, \cdot)\) | 6378.2.a.a | 1 | 1 |
6378.2.a.b | 1 | |||
6378.2.a.c | 1 | |||
6378.2.a.d | 1 | |||
6378.2.a.e | 1 | |||
6378.2.a.f | 1 | |||
6378.2.a.g | 2 | |||
6378.2.a.h | 12 | |||
6378.2.a.i | 16 | |||
6378.2.a.j | 21 | |||
6378.2.a.k | 21 | |||
6378.2.a.l | 23 | |||
6378.2.a.m | 23 | |||
6378.2.a.n | 26 | |||
6378.2.a.o | 27 | |||
6378.2.d | \(\chi_{6378}(6377, \cdot)\) | n/a | 356 | 1 |
6378.2.e | \(\chi_{6378}(343, \cdot)\) | n/a | 352 | 2 |
6378.2.h | \(\chi_{6378}(3533, \cdot)\) | n/a | 712 | 2 |
6378.2.i | \(\chi_{6378}(7, \cdot)\) | n/a | 1068 | 6 |
6378.2.j | \(\chi_{6378}(911, \cdot)\) | n/a | 2124 | 6 |
6378.2.m | \(\chi_{6378}(157, \cdot)\) | n/a | 10208 | 58 |
6378.2.n | \(\chi_{6378}(125, \cdot)\) | n/a | 20648 | 58 |
6378.2.q | \(\chi_{6378}(13, \cdot)\) | n/a | 20416 | 116 |
6378.2.r | \(\chi_{6378}(5, \cdot)\) | n/a | 41296 | 116 |
6378.2.u | \(\chi_{6378}(19, \cdot)\) | n/a | 61944 | 348 |
6378.2.x | \(\chi_{6378}(29, \cdot)\) | n/a | 123192 | 348 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6378))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(6378)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1063))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3189))\)\(^{\oplus 2}\)