Defining parameters
Level: | \( N \) | = | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(65536\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28992 | 12144 | 16848 |
Cusp forms | 28352 | 12048 | 16304 |
Eisenstein series | 640 | 96 | 544 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(384))\)
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 |
---|---|---|---|---|
384.8.a | \(\chi_{384}(1, \cdot)\) | 384.8.a.a | 1 | 1 |
384.8.a.b | 1 | |||
384.8.a.c | 1 | |||
384.8.a.d | 1 | |||
384.8.a.e | 2 | |||
384.8.a.f | 2 | |||
384.8.a.g | 2 | |||
384.8.a.h | 2 | |||
384.8.a.i | 3 | |||
384.8.a.j | 3 | |||
384.8.a.k | 3 | |||
384.8.a.l | 3 | |||
384.8.a.m | 4 | |||
384.8.a.n | 4 | |||
384.8.a.o | 4 | |||
384.8.a.p | 4 | |||
384.8.a.q | 4 | |||
384.8.a.r | 4 | |||
384.8.a.s | 4 | |||
384.8.a.t | 4 | |||
384.8.c | \(\chi_{384}(383, \cdot)\) | n/a | 112 | 1 |
384.8.d | \(\chi_{384}(193, \cdot)\) | 384.8.d.a | 6 | 1 |
384.8.d.b | 6 | |||
384.8.d.c | 8 | |||
384.8.d.d | 8 | |||
384.8.d.e | 12 | |||
384.8.d.f | 16 | |||
384.8.f | \(\chi_{384}(191, \cdot)\) | n/a | 112 | 1 |
384.8.j | \(\chi_{384}(97, \cdot)\) | n/a | 112 | 2 |
384.8.k | \(\chi_{384}(95, \cdot)\) | n/a | 216 | 2 |
384.8.n | \(\chi_{384}(49, \cdot)\) | n/a | 224 | 4 |
384.8.o | \(\chi_{384}(47, \cdot)\) | n/a | 440 | 4 |
384.8.r | \(\chi_{384}(25, \cdot)\) | None | 0 | 8 |
384.8.s | \(\chi_{384}(23, \cdot)\) | None | 0 | 8 |
384.8.v | \(\chi_{384}(13, \cdot)\) | n/a | 3584 | 16 |
384.8.w | \(\chi_{384}(11, \cdot)\) | n/a | 7136 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)