Defining parameters
| Level: | \( N \) | = | \( 165 = 3 \cdot 5 \cdot 11 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(1920\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(165))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 166 | 60 | 106 |
| Cusp forms | 6 | 4 | 2 |
| Eisenstein series | 160 | 56 | 104 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)
We only show spaces with odd 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 |
|---|---|---|---|---|
| 165.1.b | \(\chi_{165}(76, \cdot)\) | None | 0 | 1 |
| 165.1.e | \(\chi_{165}(56, \cdot)\) | None | 0 | 1 |
| 165.1.g | \(\chi_{165}(89, \cdot)\) | None | 0 | 1 |
| 165.1.h | \(\chi_{165}(109, \cdot)\) | None | 0 | 1 |
| 165.1.i | \(\chi_{165}(67, \cdot)\) | None | 0 | 2 |
| 165.1.l | \(\chi_{165}(32, \cdot)\) | 165.1.l.a | 2 | 2 |
| 165.1.l.b | 2 | |||
| 165.1.n | \(\chi_{165}(19, \cdot)\) | None | 0 | 4 |
| 165.1.o | \(\chi_{165}(14, \cdot)\) | None | 0 | 4 |
| 165.1.q | \(\chi_{165}(26, \cdot)\) | None | 0 | 4 |
| 165.1.t | \(\chi_{165}(46, \cdot)\) | None | 0 | 4 |
| 165.1.u | \(\chi_{165}(2, \cdot)\) | None | 0 | 8 |
| 165.1.x | \(\chi_{165}(37, \cdot)\) | None | 0 | 8 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 1}\)