Defining parameters
Level: | \( N \) | = | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | = | \( 7 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(229376\) | ||
Trace bound: | \(49\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(768))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 99008 | 41576 | 57432 |
Cusp forms | 97600 | 41368 | 56232 |
Eisenstein series | 1408 | 208 | 1200 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(768))\)
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 |
---|---|---|---|---|
768.7.b | \(\chi_{768}(127, \cdot)\) | 768.7.b.a | 4 | 1 |
768.7.b.b | 4 | |||
768.7.b.c | 4 | |||
768.7.b.d | 4 | |||
768.7.b.e | 4 | |||
768.7.b.f | 8 | |||
768.7.b.g | 8 | |||
768.7.b.h | 12 | |||
768.7.b.i | 24 | |||
768.7.b.j | 24 | |||
768.7.e | \(\chi_{768}(257, \cdot)\) | n/a | 188 | 1 |
768.7.g | \(\chi_{768}(511, \cdot)\) | 768.7.g.a | 2 | 1 |
768.7.g.b | 2 | |||
768.7.g.c | 4 | |||
768.7.g.d | 4 | |||
768.7.g.e | 4 | |||
768.7.g.f | 8 | |||
768.7.g.g | 8 | |||
768.7.g.h | 8 | |||
768.7.g.i | 8 | |||
768.7.g.j | 12 | |||
768.7.g.k | 12 | |||
768.7.g.l | 24 | |||
768.7.h | \(\chi_{768}(641, \cdot)\) | n/a | 188 | 1 |
768.7.i | \(\chi_{768}(65, \cdot)\) | n/a | 384 | 2 |
768.7.l | \(\chi_{768}(319, \cdot)\) | n/a | 192 | 2 |
768.7.m | \(\chi_{768}(31, \cdot)\) | n/a | 384 | 4 |
768.7.p | \(\chi_{768}(161, \cdot)\) | n/a | 752 | 4 |
768.7.q | \(\chi_{768}(17, \cdot)\) | n/a | 1520 | 8 |
768.7.t | \(\chi_{768}(79, \cdot)\) | n/a | 768 | 8 |
768.7.u | \(\chi_{768}(7, \cdot)\) | None | 0 | 16 |
768.7.x | \(\chi_{768}(41, \cdot)\) | None | 0 | 16 |
768.7.y | \(\chi_{768}(5, \cdot)\) | n/a | 24512 | 32 |
768.7.bb | \(\chi_{768}(19, \cdot)\) | n/a | 12288 | 32 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(768))\) into lower level spaces
\( S_{7}^{\mathrm{old}}(\Gamma_1(768)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 7}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 5}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)