Defining parameters
Level: | \( N \) | = | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(92160\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(462))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40800 | 9496 | 31304 |
Cusp forms | 39840 | 9496 | 30344 |
Eisenstein series | 960 | 0 | 960 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(462))\)
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 |
---|---|---|---|---|
462.8.a | \(\chi_{462}(1, \cdot)\) | 462.8.a.a | 1 | 1 |
462.8.a.b | 3 | |||
462.8.a.c | 3 | |||
462.8.a.d | 4 | |||
462.8.a.e | 4 | |||
462.8.a.f | 4 | |||
462.8.a.g | 4 | |||
462.8.a.h | 4 | |||
462.8.a.i | 4 | |||
462.8.a.j | 5 | |||
462.8.a.k | 5 | |||
462.8.a.l | 5 | |||
462.8.a.m | 5 | |||
462.8.a.n | 5 | |||
462.8.a.o | 5 | |||
462.8.a.p | 5 | |||
462.8.a.q | 6 | |||
462.8.c | \(\chi_{462}(197, \cdot)\) | n/a | 168 | 1 |
462.8.e | \(\chi_{462}(307, \cdot)\) | n/a | 112 | 1 |
462.8.g | \(\chi_{462}(419, \cdot)\) | n/a | 184 | 1 |
462.8.i | \(\chi_{462}(67, \cdot)\) | n/a | 184 | 2 |
462.8.j | \(\chi_{462}(169, \cdot)\) | n/a | 336 | 4 |
462.8.k | \(\chi_{462}(89, \cdot)\) | n/a | 376 | 2 |
462.8.n | \(\chi_{462}(65, \cdot)\) | n/a | 448 | 2 |
462.8.p | \(\chi_{462}(241, \cdot)\) | n/a | 224 | 2 |
462.8.s | \(\chi_{462}(125, \cdot)\) | n/a | 896 | 4 |
462.8.u | \(\chi_{462}(13, \cdot)\) | n/a | 448 | 4 |
462.8.w | \(\chi_{462}(29, \cdot)\) | n/a | 672 | 4 |
462.8.y | \(\chi_{462}(25, \cdot)\) | n/a | 896 | 8 |
462.8.ba | \(\chi_{462}(19, \cdot)\) | n/a | 896 | 8 |
462.8.bc | \(\chi_{462}(95, \cdot)\) | n/a | 1792 | 8 |
462.8.bf | \(\chi_{462}(5, \cdot)\) | n/a | 1792 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(462))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(462)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)