Defining parameters
Level: | \( N \) | = | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(38016\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(414))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14608 | 3748 | 10860 |
Cusp forms | 13904 | 3748 | 10156 |
Eisenstein series | 704 | 0 | 704 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(414))\)
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 |
---|---|---|---|---|
414.4.a | \(\chi_{414}(1, \cdot)\) | 414.4.a.a | 1 | 1 |
414.4.a.b | 1 | |||
414.4.a.c | 1 | |||
414.4.a.d | 1 | |||
414.4.a.e | 1 | |||
414.4.a.f | 2 | |||
414.4.a.g | 2 | |||
414.4.a.h | 2 | |||
414.4.a.i | 2 | |||
414.4.a.j | 2 | |||
414.4.a.k | 2 | |||
414.4.a.l | 3 | |||
414.4.a.m | 4 | |||
414.4.a.n | 4 | |||
414.4.d | \(\chi_{414}(413, \cdot)\) | 414.4.d.a | 24 | 1 |
414.4.e | \(\chi_{414}(139, \cdot)\) | n/a | 132 | 2 |
414.4.f | \(\chi_{414}(137, \cdot)\) | n/a | 144 | 2 |
414.4.i | \(\chi_{414}(55, \cdot)\) | n/a | 300 | 10 |
414.4.j | \(\chi_{414}(17, \cdot)\) | n/a | 240 | 10 |
414.4.m | \(\chi_{414}(13, \cdot)\) | n/a | 1440 | 20 |
414.4.p | \(\chi_{414}(5, \cdot)\) | n/a | 1440 | 20 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(414))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(414)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)