Defining parameters
Level: | \( N \) | = | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(81920\) | ||
Trace bound: | \(25\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 37184 | 15600 | 21584 |
Cusp forms | 36544 | 15504 | 21040 |
Eisenstein series | 640 | 96 | 544 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(384))\)
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 |
---|---|---|---|---|
384.10.a | \(\chi_{384}(1, \cdot)\) | 384.10.a.a | 4 | 1 |
384.10.a.b | 4 | |||
384.10.a.c | 4 | |||
384.10.a.d | 4 | |||
384.10.a.e | 4 | |||
384.10.a.f | 4 | |||
384.10.a.g | 4 | |||
384.10.a.h | 4 | |||
384.10.a.i | 5 | |||
384.10.a.j | 5 | |||
384.10.a.k | 5 | |||
384.10.a.l | 5 | |||
384.10.a.m | 5 | |||
384.10.a.n | 5 | |||
384.10.a.o | 5 | |||
384.10.a.p | 5 | |||
384.10.c | \(\chi_{384}(383, \cdot)\) | n/a | 144 | 1 |
384.10.d | \(\chi_{384}(193, \cdot)\) | 384.10.d.a | 8 | 1 |
384.10.d.b | 8 | |||
384.10.d.c | 10 | |||
384.10.d.d | 10 | |||
384.10.d.e | 16 | |||
384.10.d.f | 20 | |||
384.10.f | \(\chi_{384}(191, \cdot)\) | n/a | 144 | 1 |
384.10.j | \(\chi_{384}(97, \cdot)\) | n/a | 144 | 2 |
384.10.k | \(\chi_{384}(95, \cdot)\) | n/a | 280 | 2 |
384.10.n | \(\chi_{384}(49, \cdot)\) | n/a | 288 | 4 |
384.10.o | \(\chi_{384}(47, \cdot)\) | n/a | 568 | 4 |
384.10.r | \(\chi_{384}(25, \cdot)\) | None | 0 | 8 |
384.10.s | \(\chi_{384}(23, \cdot)\) | None | 0 | 8 |
384.10.v | \(\chi_{384}(13, \cdot)\) | n/a | 4608 | 16 |
384.10.w | \(\chi_{384}(11, \cdot)\) | n/a | 9184 | 16 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)