Defining parameters
Level: | \( N \) | = | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(10368\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(144))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4720 | 2072 | 2648 |
Cusp forms | 4496 | 2032 | 2464 |
Eisenstein series | 224 | 40 | 184 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(144))\)
We only show spaces with odd 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 |
---|---|---|---|---|
144.9.b | \(\chi_{144}(55, \cdot)\) | None | 0 | 1 |
144.9.e | \(\chi_{144}(17, \cdot)\) | 144.9.e.a | 2 | 1 |
144.9.e.b | 2 | |||
144.9.e.c | 2 | |||
144.9.e.d | 2 | |||
144.9.e.e | 4 | |||
144.9.e.f | 4 | |||
144.9.g | \(\chi_{144}(127, \cdot)\) | 144.9.g.a | 1 | 1 |
144.9.g.b | 1 | |||
144.9.g.c | 2 | |||
144.9.g.d | 2 | |||
144.9.g.e | 2 | |||
144.9.g.f | 2 | |||
144.9.g.g | 2 | |||
144.9.g.h | 4 | |||
144.9.g.i | 4 | |||
144.9.h | \(\chi_{144}(89, \cdot)\) | None | 0 | 1 |
144.9.j | \(\chi_{144}(53, \cdot)\) | n/a | 128 | 2 |
144.9.m | \(\chi_{144}(19, \cdot)\) | n/a | 158 | 2 |
144.9.n | \(\chi_{144}(41, \cdot)\) | None | 0 | 2 |
144.9.o | \(\chi_{144}(31, \cdot)\) | 144.9.o.a | 32 | 2 |
144.9.o.b | 32 | |||
144.9.o.c | 32 | |||
144.9.q | \(\chi_{144}(65, \cdot)\) | 144.9.q.a | 14 | 2 |
144.9.q.b | 16 | |||
144.9.q.c | 16 | |||
144.9.q.d | 48 | |||
144.9.t | \(\chi_{144}(7, \cdot)\) | None | 0 | 2 |
144.9.v | \(\chi_{144}(43, \cdot)\) | n/a | 760 | 4 |
144.9.w | \(\chi_{144}(5, \cdot)\) | n/a | 760 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)