Defining parameters
Level: | \( N \) | = | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 6 \) | ||
Sturm bound: | \(194940\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(722))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 81729 | 26925 | 54804 |
Cusp forms | 80721 | 26925 | 53796 |
Eisenstein series | 1008 | 0 | 1008 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(722))\)
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 |
---|---|---|---|---|
722.6.a | \(\chi_{722}(1, \cdot)\) | 722.6.a.a | 1 | 1 |
722.6.a.b | 1 | |||
722.6.a.c | 2 | |||
722.6.a.d | 3 | |||
722.6.a.e | 3 | |||
722.6.a.f | 3 | |||
722.6.a.g | 4 | |||
722.6.a.h | 4 | |||
722.6.a.i | 4 | |||
722.6.a.j | 4 | |||
722.6.a.k | 6 | |||
722.6.a.l | 6 | |||
722.6.a.m | 8 | |||
722.6.a.n | 8 | |||
722.6.a.o | 12 | |||
722.6.a.p | 12 | |||
722.6.a.q | 15 | |||
722.6.a.r | 15 | |||
722.6.a.s | 16 | |||
722.6.a.t | 16 | |||
722.6.c | \(\chi_{722}(429, \cdot)\) | n/a | 286 | 2 |
722.6.e | \(\chi_{722}(99, \cdot)\) | n/a | 846 | 6 |
722.6.g | \(\chi_{722}(39, \cdot)\) | n/a | 2826 | 18 |
722.6.i | \(\chi_{722}(7, \cdot)\) | n/a | 5652 | 36 |
722.6.k | \(\chi_{722}(5, \cdot)\) | n/a | 17172 | 108 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(722))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(722)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)