Defining parameters
Level: | \( N \) | = | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | = | \( 9 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(73728\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 33088 | 13872 | 19216 |
Cusp forms | 32448 | 13776 | 18672 |
Eisenstein series | 640 | 96 | 544 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(384))\)
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 |
---|---|---|---|---|
384.9.b | \(\chi_{384}(319, \cdot)\) | 384.9.b.a | 8 | 1 |
384.9.b.b | 8 | |||
384.9.b.c | 16 | |||
384.9.b.d | 32 | |||
384.9.e | \(\chi_{384}(257, \cdot)\) | n/a | 128 | 1 |
384.9.g | \(\chi_{384}(127, \cdot)\) | 384.9.g.a | 32 | 1 |
384.9.g.b | 32 | |||
384.9.h | \(\chi_{384}(65, \cdot)\) | n/a | 128 | 1 |
384.9.i | \(\chi_{384}(161, \cdot)\) | n/a | 248 | 2 |
384.9.l | \(\chi_{384}(31, \cdot)\) | n/a | 128 | 2 |
384.9.m | \(\chi_{384}(79, \cdot)\) | n/a | 256 | 4 |
384.9.p | \(\chi_{384}(17, \cdot)\) | n/a | 504 | 4 |
384.9.q | \(\chi_{384}(41, \cdot)\) | None | 0 | 8 |
384.9.t | \(\chi_{384}(7, \cdot)\) | None | 0 | 8 |
384.9.u | \(\chi_{384}(19, \cdot)\) | n/a | 4096 | 16 |
384.9.x | \(\chi_{384}(5, \cdot)\) | n/a | 8160 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces
\( S_{9}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)