Defining parameters
Level: | \( N \) | = | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(11664\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(162))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5211 | 1344 | 3867 |
Cusp forms | 4995 | 1344 | 3651 |
Eisenstein series | 216 | 0 | 216 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(162))\)
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 |
---|---|---|---|---|
162.8.a | \(\chi_{162}(1, \cdot)\) | 162.8.a.a | 1 | 1 |
162.8.a.b | 1 | |||
162.8.a.c | 2 | |||
162.8.a.d | 2 | |||
162.8.a.e | 3 | |||
162.8.a.f | 3 | |||
162.8.a.g | 4 | |||
162.8.a.h | 4 | |||
162.8.a.i | 4 | |||
162.8.a.j | 4 | |||
162.8.c | \(\chi_{162}(55, \cdot)\) | 162.8.c.a | 2 | 2 |
162.8.c.b | 2 | |||
162.8.c.c | 2 | |||
162.8.c.d | 2 | |||
162.8.c.e | 2 | |||
162.8.c.f | 2 | |||
162.8.c.g | 2 | |||
162.8.c.h | 2 | |||
162.8.c.i | 2 | |||
162.8.c.j | 2 | |||
162.8.c.k | 2 | |||
162.8.c.l | 2 | |||
162.8.c.m | 4 | |||
162.8.c.n | 4 | |||
162.8.c.o | 4 | |||
162.8.c.p | 4 | |||
162.8.c.q | 8 | |||
162.8.c.r | 8 | |||
162.8.e | \(\chi_{162}(19, \cdot)\) | n/a | 126 | 6 |
162.8.g | \(\chi_{162}(7, \cdot)\) | n/a | 1134 | 18 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 1}\)