Defining parameters
Level: | \( N \) | = | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(11520\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(165))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4960 | 3296 | 1664 |
Cusp forms | 4640 | 3192 | 1448 |
Eisenstein series | 320 | 104 | 216 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(165))\)
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 |
---|---|---|---|---|
165.6.a | \(\chi_{165}(1, \cdot)\) | 165.6.a.a | 3 | 1 |
165.6.a.b | 3 | |||
165.6.a.c | 3 | |||
165.6.a.d | 3 | |||
165.6.a.e | 3 | |||
165.6.a.f | 5 | |||
165.6.a.g | 5 | |||
165.6.a.h | 7 | |||
165.6.c | \(\chi_{165}(34, \cdot)\) | 165.6.c.a | 26 | 1 |
165.6.c.b | 26 | |||
165.6.d | \(\chi_{165}(164, \cdot)\) | n/a | 116 | 1 |
165.6.f | \(\chi_{165}(131, \cdot)\) | 165.6.f.a | 80 | 1 |
165.6.j | \(\chi_{165}(43, \cdot)\) | n/a | 120 | 2 |
165.6.k | \(\chi_{165}(23, \cdot)\) | n/a | 200 | 2 |
165.6.m | \(\chi_{165}(16, \cdot)\) | n/a | 160 | 4 |
165.6.p | \(\chi_{165}(41, \cdot)\) | n/a | 320 | 4 |
165.6.r | \(\chi_{165}(29, \cdot)\) | n/a | 464 | 4 |
165.6.s | \(\chi_{165}(4, \cdot)\) | n/a | 240 | 4 |
165.6.v | \(\chi_{165}(38, \cdot)\) | n/a | 928 | 8 |
165.6.w | \(\chi_{165}(7, \cdot)\) | n/a | 480 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(165))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(165)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)