Defining parameters
Level: | \( N \) | = | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(168))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 154 | 24 | 130 |
Cusp forms | 10 | 4 | 6 |
Eisenstein series | 144 | 20 | 124 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)
We only show spaces with odd 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 |
---|---|---|---|---|
168.1.d | \(\chi_{168}(113, \cdot)\) | None | 0 | 1 |
168.1.e | \(\chi_{168}(83, \cdot)\) | None | 0 | 1 |
168.1.f | \(\chi_{168}(97, \cdot)\) | None | 0 | 1 |
168.1.g | \(\chi_{168}(43, \cdot)\) | None | 0 | 1 |
168.1.l | \(\chi_{168}(13, \cdot)\) | None | 0 | 1 |
168.1.m | \(\chi_{168}(127, \cdot)\) | None | 0 | 1 |
168.1.n | \(\chi_{168}(29, \cdot)\) | None | 0 | 1 |
168.1.o | \(\chi_{168}(167, \cdot)\) | None | 0 | 1 |
168.1.r | \(\chi_{168}(47, \cdot)\) | None | 0 | 2 |
168.1.s | \(\chi_{168}(53, \cdot)\) | 168.1.s.a | 2 | 2 |
168.1.s.b | 2 | |||
168.1.w | \(\chi_{168}(79, \cdot)\) | None | 0 | 2 |
168.1.x | \(\chi_{168}(61, \cdot)\) | None | 0 | 2 |
168.1.y | \(\chi_{168}(67, \cdot)\) | None | 0 | 2 |
168.1.z | \(\chi_{168}(73, \cdot)\) | None | 0 | 2 |
168.1.be | \(\chi_{168}(59, \cdot)\) | None | 0 | 2 |
168.1.bf | \(\chi_{168}(65, \cdot)\) | None | 0 | 2 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(168))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(168)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)