Defining parameters
Level: | \( N \) | = | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(12960\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(198))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5560 | 1399 | 4161 |
Cusp forms | 5240 | 1399 | 3841 |
Eisenstein series | 320 | 0 | 320 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(198))\)
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 |
---|---|---|---|---|
198.6.a | \(\chi_{198}(1, \cdot)\) | 198.6.a.a | 1 | 1 |
198.6.a.b | 1 | |||
198.6.a.c | 1 | |||
198.6.a.d | 1 | |||
198.6.a.e | 1 | |||
198.6.a.f | 1 | |||
198.6.a.g | 1 | |||
198.6.a.h | 1 | |||
198.6.a.i | 1 | |||
198.6.a.j | 2 | |||
198.6.a.k | 2 | |||
198.6.a.l | 2 | |||
198.6.a.m | 2 | |||
198.6.a.n | 2 | |||
198.6.b | \(\chi_{198}(197, \cdot)\) | 198.6.b.a | 10 | 1 |
198.6.b.b | 10 | |||
198.6.e | \(\chi_{198}(67, \cdot)\) | 198.6.e.a | 24 | 2 |
198.6.e.b | 24 | |||
198.6.e.c | 26 | |||
198.6.e.d | 26 | |||
198.6.f | \(\chi_{198}(37, \cdot)\) | 198.6.f.a | 8 | 4 |
198.6.f.b | 8 | |||
198.6.f.c | 8 | |||
198.6.f.d | 12 | |||
198.6.f.e | 12 | |||
198.6.f.f | 12 | |||
198.6.f.g | 20 | |||
198.6.f.h | 20 | |||
198.6.i | \(\chi_{198}(65, \cdot)\) | n/a | 120 | 2 |
198.6.l | \(\chi_{198}(17, \cdot)\) | 198.6.l.a | 40 | 4 |
198.6.l.b | 40 | |||
198.6.m | \(\chi_{198}(25, \cdot)\) | n/a | 480 | 8 |
198.6.n | \(\chi_{198}(29, \cdot)\) | n/a | 480 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(198))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(198)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)