Defining parameters
| Level: | \( N \) | = | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Nonzero newspaces: | \( 8 \) | ||
| Newform subspaces: | \( 26 \) | ||
| Sturm bound: | \(19008\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(414))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 5104 | 1250 | 3854 |
| Cusp forms | 4401 | 1250 | 3151 |
| Eisenstein series | 703 | 0 | 703 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(414))\)
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 |
|---|---|---|---|---|
| 414.2.a | \(\chi_{414}(1, \cdot)\) | 414.2.a.a | 1 | 1 |
| 414.2.a.b | 1 | |||
| 414.2.a.c | 1 | |||
| 414.2.a.d | 1 | |||
| 414.2.a.e | 2 | |||
| 414.2.a.f | 2 | |||
| 414.2.a.g | 2 | |||
| 414.2.d | \(\chi_{414}(413, \cdot)\) | 414.2.d.a | 8 | 1 |
| 414.2.e | \(\chi_{414}(139, \cdot)\) | 414.2.e.a | 2 | 2 |
| 414.2.e.b | 10 | |||
| 414.2.e.c | 10 | |||
| 414.2.e.d | 10 | |||
| 414.2.e.e | 12 | |||
| 414.2.f | \(\chi_{414}(137, \cdot)\) | 414.2.f.a | 48 | 2 |
| 414.2.i | \(\chi_{414}(55, \cdot)\) | 414.2.i.a | 10 | 10 |
| 414.2.i.b | 10 | |||
| 414.2.i.c | 10 | |||
| 414.2.i.d | 10 | |||
| 414.2.i.e | 10 | |||
| 414.2.i.f | 10 | |||
| 414.2.i.g | 20 | |||
| 414.2.i.h | 20 | |||
| 414.2.j | \(\chi_{414}(17, \cdot)\) | 414.2.j.a | 80 | 10 |
| 414.2.m | \(\chi_{414}(13, \cdot)\) | 414.2.m.a | 240 | 20 |
| 414.2.m.b | 240 | |||
| 414.2.p | \(\chi_{414}(5, \cdot)\) | 414.2.p.a | 480 | 20 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(414))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(414)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)