Defining parameters
Level: | \( N \) | = | \( 368 = 2^{4} \cdot 23 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(33792\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(368))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12980 | 7195 | 5785 |
Cusp forms | 12364 | 7007 | 5357 |
Eisenstein series | 616 | 188 | 428 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)
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 |
---|---|---|---|---|
368.4.a | \(\chi_{368}(1, \cdot)\) | 368.4.a.a | 1 | 1 |
368.4.a.b | 1 | |||
368.4.a.c | 1 | |||
368.4.a.d | 1 | |||
368.4.a.e | 1 | |||
368.4.a.f | 2 | |||
368.4.a.g | 2 | |||
368.4.a.h | 3 | |||
368.4.a.i | 3 | |||
368.4.a.j | 3 | |||
368.4.a.k | 3 | |||
368.4.a.l | 4 | |||
368.4.a.m | 4 | |||
368.4.a.n | 4 | |||
368.4.b | \(\chi_{368}(185, \cdot)\) | None | 0 | 1 |
368.4.c | \(\chi_{368}(367, \cdot)\) | 368.4.c.a | 12 | 1 |
368.4.c.b | 24 | |||
368.4.h | \(\chi_{368}(183, \cdot)\) | None | 0 | 1 |
368.4.i | \(\chi_{368}(91, \cdot)\) | n/a | 284 | 2 |
368.4.j | \(\chi_{368}(93, \cdot)\) | n/a | 264 | 2 |
368.4.m | \(\chi_{368}(49, \cdot)\) | n/a | 350 | 10 |
368.4.n | \(\chi_{368}(7, \cdot)\) | None | 0 | 10 |
368.4.s | \(\chi_{368}(15, \cdot)\) | n/a | 360 | 10 |
368.4.t | \(\chi_{368}(9, \cdot)\) | None | 0 | 10 |
368.4.w | \(\chi_{368}(13, \cdot)\) | n/a | 2840 | 20 |
368.4.x | \(\chi_{368}(11, \cdot)\) | n/a | 2840 | 20 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(368))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)