Defining parameters
| Level: | \( N \) | = | \( 192 = 2^{6} \cdot 3 \) |
| Weight: | \( k \) | = | \( 5 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Sturm bound: | \(10240\) | ||
| Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(192))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 4240 | 1750 | 2490 |
| Cusp forms | 3952 | 1706 | 2246 |
| Eisenstein series | 288 | 44 | 244 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(192))\)
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 |
|---|---|---|---|---|
| 192.5.b | \(\chi_{192}(31, \cdot)\) | 192.5.b.a | 4 | 1 |
| 192.5.b.b | 4 | |||
| 192.5.b.c | 8 | |||
| 192.5.e | \(\chi_{192}(65, \cdot)\) | 192.5.e.a | 1 | 1 |
| 192.5.e.b | 1 | |||
| 192.5.e.c | 2 | |||
| 192.5.e.d | 2 | |||
| 192.5.e.e | 4 | |||
| 192.5.e.f | 4 | |||
| 192.5.e.g | 8 | |||
| 192.5.e.h | 8 | |||
| 192.5.g | \(\chi_{192}(127, \cdot)\) | 192.5.g.a | 2 | 1 |
| 192.5.g.b | 2 | |||
| 192.5.g.c | 4 | |||
| 192.5.g.d | 4 | |||
| 192.5.g.e | 4 | |||
| 192.5.h | \(\chi_{192}(161, \cdot)\) | 192.5.h.a | 4 | 1 |
| 192.5.h.b | 4 | |||
| 192.5.h.c | 8 | |||
| 192.5.h.d | 16 | |||
| 192.5.i | \(\chi_{192}(17, \cdot)\) | 192.5.i.a | 60 | 2 |
| 192.5.l | \(\chi_{192}(79, \cdot)\) | 192.5.l.a | 32 | 2 |
| 192.5.m | \(\chi_{192}(7, \cdot)\) | None | 0 | 4 |
| 192.5.p | \(\chi_{192}(41, \cdot)\) | None | 0 | 4 |
| 192.5.q | \(\chi_{192}(5, \cdot)\) | n/a | 1008 | 8 |
| 192.5.t | \(\chi_{192}(19, \cdot)\) | n/a | 512 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces
\( S_{5}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 1}\)