Defining parameters
Level: | \( N \) | = | \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(10368\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(180))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4480 | 1859 | 2621 |
Cusp forms | 4160 | 1803 | 2357 |
Eisenstein series | 320 | 56 | 264 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(180))\)
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 |
---|---|---|---|---|
180.6.a | \(\chi_{180}(1, \cdot)\) | 180.6.a.a | 1 | 1 |
180.6.a.b | 1 | |||
180.6.a.c | 1 | |||
180.6.a.d | 1 | |||
180.6.a.e | 1 | |||
180.6.a.f | 2 | |||
180.6.a.g | 2 | |||
180.6.d | \(\chi_{180}(109, \cdot)\) | 180.6.d.a | 2 | 1 |
180.6.d.b | 2 | |||
180.6.d.c | 2 | |||
180.6.d.d | 6 | |||
180.6.e | \(\chi_{180}(71, \cdot)\) | 180.6.e.a | 40 | 1 |
180.6.h | \(\chi_{180}(179, \cdot)\) | 180.6.h.a | 4 | 1 |
180.6.h.b | 56 | |||
180.6.i | \(\chi_{180}(61, \cdot)\) | 180.6.i.a | 18 | 2 |
180.6.i.b | 22 | |||
180.6.j | \(\chi_{180}(17, \cdot)\) | 180.6.j.a | 20 | 2 |
180.6.k | \(\chi_{180}(127, \cdot)\) | n/a | 146 | 2 |
180.6.n | \(\chi_{180}(59, \cdot)\) | n/a | 352 | 2 |
180.6.q | \(\chi_{180}(11, \cdot)\) | n/a | 240 | 2 |
180.6.r | \(\chi_{180}(49, \cdot)\) | 180.6.r.a | 60 | 2 |
180.6.w | \(\chi_{180}(77, \cdot)\) | n/a | 120 | 4 |
180.6.x | \(\chi_{180}(7, \cdot)\) | n/a | 704 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(180)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)