Defining parameters
Level: | \( N \) | = | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(16384\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(192))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7312 | 3046 | 4266 |
Cusp forms | 7024 | 3002 | 4022 |
Eisenstein series | 288 | 44 | 244 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(192))\)
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 |
---|---|---|---|---|
192.8.a | \(\chi_{192}(1, \cdot)\) | 192.8.a.a | 1 | 1 |
192.8.a.b | 1 | |||
192.8.a.c | 1 | |||
192.8.a.d | 1 | |||
192.8.a.e | 1 | |||
192.8.a.f | 1 | |||
192.8.a.g | 1 | |||
192.8.a.h | 1 | |||
192.8.a.i | 1 | |||
192.8.a.j | 1 | |||
192.8.a.k | 1 | |||
192.8.a.l | 1 | |||
192.8.a.m | 1 | |||
192.8.a.n | 1 | |||
192.8.a.o | 1 | |||
192.8.a.p | 1 | |||
192.8.a.q | 2 | |||
192.8.a.r | 2 | |||
192.8.a.s | 2 | |||
192.8.a.t | 2 | |||
192.8.a.u | 2 | |||
192.8.a.v | 2 | |||
192.8.c | \(\chi_{192}(191, \cdot)\) | 192.8.c.a | 2 | 1 |
192.8.c.b | 4 | |||
192.8.c.c | 4 | |||
192.8.c.d | 8 | |||
192.8.c.e | 8 | |||
192.8.c.f | 28 | |||
192.8.d | \(\chi_{192}(97, \cdot)\) | 192.8.d.a | 4 | 1 |
192.8.d.b | 4 | |||
192.8.d.c | 8 | |||
192.8.d.d | 12 | |||
192.8.f | \(\chi_{192}(95, \cdot)\) | 192.8.f.a | 4 | 1 |
192.8.f.b | 4 | |||
192.8.f.c | 16 | |||
192.8.f.d | 32 | |||
192.8.j | \(\chi_{192}(49, \cdot)\) | 192.8.j.a | 56 | 2 |
192.8.k | \(\chi_{192}(47, \cdot)\) | n/a | 108 | 2 |
192.8.n | \(\chi_{192}(25, \cdot)\) | None | 0 | 4 |
192.8.o | \(\chi_{192}(23, \cdot)\) | None | 0 | 4 |
192.8.r | \(\chi_{192}(13, \cdot)\) | n/a | 896 | 8 |
192.8.s | \(\chi_{192}(11, \cdot)\) | n/a | 1776 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(192))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(192)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 7}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)