Defining parameters
Level: | \( N \) | = | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(8064\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(144))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3568 | 1559 | 2009 |
Cusp forms | 3344 | 1519 | 1825 |
Eisenstein series | 224 | 40 | 184 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(144))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
144.7.b | \(\chi_{144}(55, \cdot)\) | None | 0 | 1 |
144.7.e | \(\chi_{144}(17, \cdot)\) | 144.7.e.a | 2 | 1 |
144.7.e.b | 2 | |||
144.7.e.c | 2 | |||
144.7.e.d | 2 | |||
144.7.e.e | 4 | |||
144.7.g | \(\chi_{144}(127, \cdot)\) | 144.7.g.a | 1 | 1 |
144.7.g.b | 2 | |||
144.7.g.c | 2 | |||
144.7.g.d | 2 | |||
144.7.g.e | 2 | |||
144.7.g.f | 2 | |||
144.7.g.g | 4 | |||
144.7.h | \(\chi_{144}(89, \cdot)\) | None | 0 | 1 |
144.7.j | \(\chi_{144}(53, \cdot)\) | 144.7.j.a | 96 | 2 |
144.7.m | \(\chi_{144}(19, \cdot)\) | n/a | 118 | 2 |
144.7.n | \(\chi_{144}(41, \cdot)\) | None | 0 | 2 |
144.7.o | \(\chi_{144}(31, \cdot)\) | 144.7.o.a | 24 | 2 |
144.7.o.b | 24 | |||
144.7.o.c | 24 | |||
144.7.q | \(\chi_{144}(65, \cdot)\) | 144.7.q.a | 10 | 2 |
144.7.q.b | 12 | |||
144.7.q.c | 12 | |||
144.7.q.d | 36 | |||
144.7.t | \(\chi_{144}(7, \cdot)\) | None | 0 | 2 |
144.7.v | \(\chi_{144}(43, \cdot)\) | n/a | 568 | 4 |
144.7.w | \(\chi_{144}(5, \cdot)\) | n/a | 568 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(144))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(144)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)