Defining parameters
Level: | \( N \) | = | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(75264\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(392))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 33288 | 17872 | 15416 |
Cusp forms | 32568 | 17678 | 14890 |
Eisenstein series | 720 | 194 | 526 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(392))\)
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 |
---|---|---|---|---|
392.8.a | \(\chi_{392}(1, \cdot)\) | 392.8.a.a | 1 | 1 |
392.8.a.b | 1 | |||
392.8.a.c | 1 | |||
392.8.a.d | 1 | |||
392.8.a.e | 2 | |||
392.8.a.f | 3 | |||
392.8.a.g | 3 | |||
392.8.a.h | 4 | |||
392.8.a.i | 6 | |||
392.8.a.j | 7 | |||
392.8.a.k | 7 | |||
392.8.a.l | 7 | |||
392.8.a.m | 7 | |||
392.8.a.n | 10 | |||
392.8.a.o | 12 | |||
392.8.b | \(\chi_{392}(197, \cdot)\) | n/a | 282 | 1 |
392.8.e | \(\chi_{392}(195, \cdot)\) | n/a | 276 | 1 |
392.8.f | \(\chi_{392}(391, \cdot)\) | None | 0 | 1 |
392.8.i | \(\chi_{392}(177, \cdot)\) | n/a | 140 | 2 |
392.8.l | \(\chi_{392}(31, \cdot)\) | None | 0 | 2 |
392.8.m | \(\chi_{392}(19, \cdot)\) | n/a | 552 | 2 |
392.8.p | \(\chi_{392}(165, \cdot)\) | n/a | 552 | 2 |
392.8.q | \(\chi_{392}(57, \cdot)\) | n/a | 588 | 6 |
392.8.t | \(\chi_{392}(55, \cdot)\) | None | 0 | 6 |
392.8.u | \(\chi_{392}(27, \cdot)\) | n/a | 2340 | 6 |
392.8.x | \(\chi_{392}(29, \cdot)\) | n/a | 2340 | 6 |
392.8.y | \(\chi_{392}(9, \cdot)\) | n/a | 1176 | 12 |
392.8.z | \(\chi_{392}(37, \cdot)\) | n/a | 4680 | 12 |
392.8.bc | \(\chi_{392}(3, \cdot)\) | n/a | 4680 | 12 |
392.8.bd | \(\chi_{392}(47, \cdot)\) | None | 0 | 12 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(392))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(392)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)