Defining parameters
Level: | \( N \) | = | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(57344\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24896 | 10416 | 14480 |
Cusp forms | 24256 | 10320 | 13936 |
Eisenstein series | 640 | 96 | 544 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(384))\)
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 |
---|---|---|---|---|
384.7.b | \(\chi_{384}(319, \cdot)\) | 384.7.b.a | 4 | 1 |
384.7.b.b | 4 | |||
384.7.b.c | 8 | |||
384.7.b.d | 8 | |||
384.7.b.e | 24 | |||
384.7.e | \(\chi_{384}(257, \cdot)\) | 384.7.e.a | 24 | 1 |
384.7.e.b | 24 | |||
384.7.e.c | 24 | |||
384.7.e.d | 24 | |||
384.7.g | \(\chi_{384}(127, \cdot)\) | 384.7.g.a | 24 | 1 |
384.7.g.b | 24 | |||
384.7.h | \(\chi_{384}(65, \cdot)\) | 384.7.h.a | 2 | 1 |
384.7.h.b | 2 | |||
384.7.h.c | 2 | |||
384.7.h.d | 2 | |||
384.7.h.e | 8 | |||
384.7.h.f | 8 | |||
384.7.h.g | 24 | |||
384.7.h.h | 48 | |||
384.7.i | \(\chi_{384}(161, \cdot)\) | n/a | 184 | 2 |
384.7.l | \(\chi_{384}(31, \cdot)\) | 384.7.l.a | 48 | 2 |
384.7.l.b | 48 | |||
384.7.m | \(\chi_{384}(79, \cdot)\) | n/a | 192 | 4 |
384.7.p | \(\chi_{384}(17, \cdot)\) | n/a | 376 | 4 |
384.7.q | \(\chi_{384}(41, \cdot)\) | None | 0 | 8 |
384.7.t | \(\chi_{384}(7, \cdot)\) | None | 0 | 8 |
384.7.u | \(\chi_{384}(19, \cdot)\) | n/a | 3072 | 16 |
384.7.x | \(\chi_{384}(5, \cdot)\) | n/a | 6112 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)