Defining parameters
Level: | \( N \) | = | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 16 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(18432\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(144))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8752 | 3868 | 4884 |
Cusp forms | 8528 | 3827 | 4701 |
Eisenstein series | 224 | 41 | 183 |
Trace form
Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(144))\)
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 |
---|---|---|---|---|
144.16.a | \(\chi_{144}(1, \cdot)\) | 144.16.a.a | 1 | 1 |
144.16.a.b | 1 | |||
144.16.a.c | 1 | |||
144.16.a.d | 1 | |||
144.16.a.e | 1 | |||
144.16.a.f | 1 | |||
144.16.a.g | 1 | |||
144.16.a.h | 1 | |||
144.16.a.i | 1 | |||
144.16.a.j | 1 | |||
144.16.a.k | 1 | |||
144.16.a.l | 1 | |||
144.16.a.m | 1 | |||
144.16.a.n | 1 | |||
144.16.a.o | 1 | |||
144.16.a.p | 2 | |||
144.16.a.q | 2 | |||
144.16.a.r | 2 | |||
144.16.a.s | 2 | |||
144.16.a.t | 2 | |||
144.16.a.u | 2 | |||
144.16.a.v | 2 | |||
144.16.a.w | 4 | |||
144.16.a.x | 4 | |||
144.16.c | \(\chi_{144}(143, \cdot)\) | 144.16.c.a | 2 | 1 |
144.16.c.b | 8 | |||
144.16.c.c | 20 | |||
144.16.d | \(\chi_{144}(73, \cdot)\) | None | 0 | 1 |
144.16.f | \(\chi_{144}(71, \cdot)\) | None | 0 | 1 |
144.16.i | \(\chi_{144}(49, \cdot)\) | n/a | 178 | 2 |
144.16.k | \(\chi_{144}(37, \cdot)\) | n/a | 298 | 2 |
144.16.l | \(\chi_{144}(35, \cdot)\) | n/a | 240 | 2 |
144.16.p | \(\chi_{144}(23, \cdot)\) | None | 0 | 2 |
144.16.r | \(\chi_{144}(25, \cdot)\) | None | 0 | 2 |
144.16.s | \(\chi_{144}(47, \cdot)\) | n/a | 180 | 2 |
144.16.u | \(\chi_{144}(11, \cdot)\) | n/a | 1432 | 4 |
144.16.x | \(\chi_{144}(13, \cdot)\) | n/a | 1432 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces
\( S_{16}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)