Defining parameters
Level: | \( N \) | = | \( 1083 = 3 \cdot 19^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(346560\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1083))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 130968 | 97398 | 33570 |
Cusp forms | 128952 | 96462 | 32490 |
Eisenstein series | 2016 | 936 | 1080 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1083))\)
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 |
---|---|---|---|---|
1083.4.a | \(\chi_{1083}(1, \cdot)\) | 1083.4.a.a | 1 | 1 |
1083.4.a.b | 2 | |||
1083.4.a.c | 3 | |||
1083.4.a.d | 4 | |||
1083.4.a.e | 4 | |||
1083.4.a.f | 4 | |||
1083.4.a.g | 5 | |||
1083.4.a.h | 5 | |||
1083.4.a.i | 5 | |||
1083.4.a.j | 5 | |||
1083.4.a.k | 10 | |||
1083.4.a.l | 10 | |||
1083.4.a.m | 10 | |||
1083.4.a.n | 10 | |||
1083.4.a.o | 12 | |||
1083.4.a.p | 12 | |||
1083.4.a.q | 16 | |||
1083.4.a.r | 16 | |||
1083.4.a.s | 18 | |||
1083.4.a.t | 18 | |||
1083.4.d | \(\chi_{1083}(1082, \cdot)\) | n/a | 324 | 1 |
1083.4.e | \(\chi_{1083}(292, \cdot)\) | n/a | 340 | 2 |
1083.4.f | \(\chi_{1083}(293, \cdot)\) | n/a | 648 | 2 |
1083.4.i | \(\chi_{1083}(28, \cdot)\) | n/a | 1020 | 6 |
1083.4.j | \(\chi_{1083}(116, \cdot)\) | n/a | 1944 | 6 |
1083.4.m | \(\chi_{1083}(58, \cdot)\) | n/a | 3420 | 18 |
1083.4.n | \(\chi_{1083}(56, \cdot)\) | n/a | 6804 | 18 |
1083.4.q | \(\chi_{1083}(7, \cdot)\) | n/a | 6840 | 36 |
1083.4.t | \(\chi_{1083}(8, \cdot)\) | n/a | 13608 | 36 |
1083.4.u | \(\chi_{1083}(4, \cdot)\) | n/a | 20520 | 108 |
1083.4.x | \(\chi_{1083}(2, \cdot)\) | n/a | 40824 | 108 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1083))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1083)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)