Defining parameters
Level: | \( N \) | = | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(519840\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2166))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 131976 | 32309 | 99667 |
Cusp forms | 127945 | 32309 | 95636 |
Eisenstein series | 4031 | 0 | 4031 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2166))\)
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 |
---|---|---|---|---|
2166.2.a | \(\chi_{2166}(1, \cdot)\) | 2166.2.a.a | 1 | 1 |
2166.2.a.b | 1 | |||
2166.2.a.c | 1 | |||
2166.2.a.d | 1 | |||
2166.2.a.e | 1 | |||
2166.2.a.f | 1 | |||
2166.2.a.g | 1 | |||
2166.2.a.h | 1 | |||
2166.2.a.i | 1 | |||
2166.2.a.j | 2 | |||
2166.2.a.k | 2 | |||
2166.2.a.l | 2 | |||
2166.2.a.m | 2 | |||
2166.2.a.n | 3 | |||
2166.2.a.o | 3 | |||
2166.2.a.p | 3 | |||
2166.2.a.q | 3 | |||
2166.2.a.r | 3 | |||
2166.2.a.s | 3 | |||
2166.2.a.t | 3 | |||
2166.2.a.u | 3 | |||
2166.2.a.v | 4 | |||
2166.2.a.w | 4 | |||
2166.2.a.x | 4 | |||
2166.2.a.y | 4 | |||
2166.2.b | \(\chi_{2166}(2165, \cdot)\) | n/a | 112 | 1 |
2166.2.e | \(\chi_{2166}(1375, \cdot)\) | n/a | 116 | 2 |
2166.2.h | \(\chi_{2166}(293, \cdot)\) | n/a | 224 | 2 |
2166.2.i | \(\chi_{2166}(415, \cdot)\) | n/a | 336 | 6 |
2166.2.l | \(\chi_{2166}(299, \cdot)\) | n/a | 684 | 6 |
2166.2.m | \(\chi_{2166}(115, \cdot)\) | n/a | 1116 | 18 |
2166.2.p | \(\chi_{2166}(113, \cdot)\) | n/a | 2304 | 18 |
2166.2.q | \(\chi_{2166}(7, \cdot)\) | n/a | 2232 | 36 |
2166.2.r | \(\chi_{2166}(65, \cdot)\) | n/a | 4608 | 36 |
2166.2.u | \(\chi_{2166}(25, \cdot)\) | n/a | 6912 | 108 |
2166.2.v | \(\chi_{2166}(29, \cdot)\) | n/a | 13608 | 108 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2166))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)