Defining parameters
Level: | \( N \) | = | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(30720\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(231))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13680 | 9584 | 4096 |
Cusp forms | 13200 | 9408 | 3792 |
Eisenstein series | 480 | 176 | 304 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(231))\)
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 |
---|---|---|---|---|
231.8.a | \(\chi_{231}(1, \cdot)\) | 231.8.a.a | 7 | 1 |
231.8.a.b | 7 | |||
231.8.a.c | 7 | |||
231.8.a.d | 7 | |||
231.8.a.e | 10 | |||
231.8.a.f | 10 | |||
231.8.a.g | 10 | |||
231.8.a.h | 10 | |||
231.8.c | \(\chi_{231}(76, \cdot)\) | n/a | 112 | 1 |
231.8.e | \(\chi_{231}(188, \cdot)\) | n/a | 188 | 1 |
231.8.g | \(\chi_{231}(197, \cdot)\) | n/a | 168 | 1 |
231.8.i | \(\chi_{231}(67, \cdot)\) | n/a | 188 | 2 |
231.8.j | \(\chi_{231}(64, \cdot)\) | n/a | 336 | 4 |
231.8.l | \(\chi_{231}(32, \cdot)\) | n/a | 440 | 2 |
231.8.n | \(\chi_{231}(89, \cdot)\) | n/a | 372 | 2 |
231.8.p | \(\chi_{231}(10, \cdot)\) | n/a | 224 | 2 |
231.8.s | \(\chi_{231}(8, \cdot)\) | n/a | 672 | 4 |
231.8.u | \(\chi_{231}(20, \cdot)\) | n/a | 880 | 4 |
231.8.w | \(\chi_{231}(13, \cdot)\) | n/a | 448 | 4 |
231.8.y | \(\chi_{231}(4, \cdot)\) | n/a | 896 | 8 |
231.8.ba | \(\chi_{231}(19, \cdot)\) | n/a | 896 | 8 |
231.8.bc | \(\chi_{231}(5, \cdot)\) | n/a | 1760 | 8 |
231.8.be | \(\chi_{231}(2, \cdot)\) | n/a | 1760 | 8 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(231)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)