Defining parameters
Level: | \( N \) | = | \( 396 = 2^{2} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(51840\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(396))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22000 | 9893 | 12107 |
Cusp forms | 21200 | 9729 | 11471 |
Eisenstein series | 800 | 164 | 636 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(396))\)
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 |
---|---|---|---|---|
396.6.a | \(\chi_{396}(1, \cdot)\) | 396.6.a.a | 1 | 1 |
396.6.a.b | 1 | |||
396.6.a.c | 1 | |||
396.6.a.d | 1 | |||
396.6.a.e | 1 | |||
396.6.a.f | 2 | |||
396.6.a.g | 3 | |||
396.6.a.h | 3 | |||
396.6.a.i | 4 | |||
396.6.a.j | 4 | |||
396.6.b | \(\chi_{396}(197, \cdot)\) | 396.6.b.a | 20 | 1 |
396.6.c | \(\chi_{396}(287, \cdot)\) | 396.6.c.a | 50 | 1 |
396.6.c.b | 50 | |||
396.6.h | \(\chi_{396}(307, \cdot)\) | n/a | 148 | 1 |
396.6.i | \(\chi_{396}(133, \cdot)\) | 396.6.i.a | 48 | 2 |
396.6.i.b | 52 | |||
396.6.j | \(\chi_{396}(37, \cdot)\) | 396.6.j.a | 4 | 4 |
396.6.j.b | 16 | |||
396.6.j.c | 20 | |||
396.6.j.d | 20 | |||
396.6.j.e | 40 | |||
396.6.k | \(\chi_{396}(43, \cdot)\) | n/a | 712 | 2 |
396.6.p | \(\chi_{396}(23, \cdot)\) | n/a | 600 | 2 |
396.6.q | \(\chi_{396}(65, \cdot)\) | n/a | 120 | 2 |
396.6.r | \(\chi_{396}(19, \cdot)\) | n/a | 592 | 4 |
396.6.w | \(\chi_{396}(71, \cdot)\) | n/a | 480 | 4 |
396.6.x | \(\chi_{396}(17, \cdot)\) | 396.6.x.a | 80 | 4 |
396.6.y | \(\chi_{396}(25, \cdot)\) | n/a | 480 | 8 |
396.6.z | \(\chi_{396}(29, \cdot)\) | n/a | 480 | 8 |
396.6.ba | \(\chi_{396}(47, \cdot)\) | n/a | 2848 | 8 |
396.6.bf | \(\chi_{396}(7, \cdot)\) | n/a | 2848 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(396))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(396)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 1}\)