Defining parameters
Level: | \( N \) | = | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 22 \) | ||
Sturm bound: | \(5832\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(162))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2295 | 576 | 1719 |
Cusp forms | 2079 | 576 | 1503 |
Eisenstein series | 216 | 0 | 216 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(162))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
162.4.a | \(\chi_{162}(1, \cdot)\) | 162.4.a.a | 1 | 1 |
162.4.a.b | 1 | |||
162.4.a.c | 1 | |||
162.4.a.d | 1 | |||
162.4.a.e | 2 | |||
162.4.a.f | 2 | |||
162.4.a.g | 2 | |||
162.4.a.h | 2 | |||
162.4.c | \(\chi_{162}(55, \cdot)\) | 162.4.c.a | 2 | 2 |
162.4.c.b | 2 | |||
162.4.c.c | 2 | |||
162.4.c.d | 2 | |||
162.4.c.e | 2 | |||
162.4.c.f | 2 | |||
162.4.c.g | 2 | |||
162.4.c.h | 2 | |||
162.4.c.i | 4 | |||
162.4.c.j | 4 | |||
162.4.e | \(\chi_{162}(19, \cdot)\) | 162.4.e.a | 24 | 6 |
162.4.e.b | 30 | |||
162.4.g | \(\chi_{162}(7, \cdot)\) | 162.4.g.a | 234 | 18 |
162.4.g.b | 252 |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(162))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(162)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)