Defining parameters
Level: | \( N \) | = | \( 676 = 2^{2} \cdot 13^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(170352\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(676))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 71550 | 41120 | 30430 |
Cusp forms | 70410 | 40712 | 29698 |
Eisenstein series | 1140 | 408 | 732 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(676))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
676.6.a | \(\chi_{676}(1, \cdot)\) | 676.6.a.a | 1 | 1 |
676.6.a.b | 1 | |||
676.6.a.c | 1 | |||
676.6.a.d | 3 | |||
676.6.a.e | 6 | |||
676.6.a.f | 6 | |||
676.6.a.g | 6 | |||
676.6.a.h | 10 | |||
676.6.a.i | 15 | |||
676.6.a.j | 15 | |||
676.6.d | \(\chi_{676}(337, \cdot)\) | 676.6.d.a | 2 | 1 |
676.6.d.b | 2 | |||
676.6.d.c | 2 | |||
676.6.d.d | 6 | |||
676.6.d.e | 10 | |||
676.6.d.f | 12 | |||
676.6.d.g | 30 | |||
676.6.e | \(\chi_{676}(529, \cdot)\) | n/a | 128 | 2 |
676.6.f | \(\chi_{676}(99, \cdot)\) | n/a | 750 | 2 |
676.6.h | \(\chi_{676}(361, \cdot)\) | n/a | 130 | 2 |
676.6.l | \(\chi_{676}(19, \cdot)\) | n/a | 1500 | 4 |
676.6.m | \(\chi_{676}(53, \cdot)\) | n/a | 924 | 12 |
676.6.n | \(\chi_{676}(25, \cdot)\) | n/a | 912 | 12 |
676.6.q | \(\chi_{676}(9, \cdot)\) | n/a | 1824 | 24 |
676.6.s | \(\chi_{676}(31, \cdot)\) | n/a | 10872 | 24 |
676.6.v | \(\chi_{676}(17, \cdot)\) | n/a | 1800 | 24 |
676.6.w | \(\chi_{676}(7, \cdot)\) | n/a | 21744 | 48 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)