Defining parameters
Level: | \( N \) | = | \( 368 = 2^{4} \cdot 23 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(50688\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(368))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21428 | 11929 | 9499 |
Cusp forms | 20812 | 11741 | 9071 |
Eisenstein series | 616 | 188 | 428 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(368))\)
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 |
---|---|---|---|---|
368.6.a | \(\chi_{368}(1, \cdot)\) | 368.6.a.a | 2 | 1 |
368.6.a.b | 2 | |||
368.6.a.c | 3 | |||
368.6.a.d | 3 | |||
368.6.a.e | 3 | |||
368.6.a.f | 4 | |||
368.6.a.g | 4 | |||
368.6.a.h | 6 | |||
368.6.a.i | 6 | |||
368.6.a.j | 7 | |||
368.6.a.k | 7 | |||
368.6.a.l | 8 | |||
368.6.b | \(\chi_{368}(185, \cdot)\) | None | 0 | 1 |
368.6.c | \(\chi_{368}(367, \cdot)\) | 368.6.c.a | 20 | 1 |
368.6.c.b | 40 | |||
368.6.h | \(\chi_{368}(183, \cdot)\) | None | 0 | 1 |
368.6.i | \(\chi_{368}(91, \cdot)\) | n/a | 476 | 2 |
368.6.j | \(\chi_{368}(93, \cdot)\) | n/a | 440 | 2 |
368.6.m | \(\chi_{368}(49, \cdot)\) | n/a | 590 | 10 |
368.6.n | \(\chi_{368}(7, \cdot)\) | None | 0 | 10 |
368.6.s | \(\chi_{368}(15, \cdot)\) | n/a | 600 | 10 |
368.6.t | \(\chi_{368}(9, \cdot)\) | None | 0 | 10 |
368.6.w | \(\chi_{368}(13, \cdot)\) | n/a | 4760 | 20 |
368.6.x | \(\chi_{368}(11, \cdot)\) | n/a | 4760 | 20 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)