Defining parameters
Level: | \( N \) | = | \( 1127 = 7^{2} \cdot 23 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 14 \) | ||
Sturm bound: | \(103488\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1127))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1425 | 1101 | 324 |
Cusp forms | 105 | 82 | 23 |
Eisenstein series | 1320 | 1019 | 301 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 82 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1127))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
1127.1.b | \(\chi_{1127}(783, \cdot)\) | None | 0 | 1 |
1127.1.d | \(\chi_{1127}(344, \cdot)\) | 1127.1.d.a | 1 | 1 |
1127.1.d.b | 1 | |||
1127.1.d.c | 2 | |||
1127.1.d.d | 2 | |||
1127.1.d.e | 4 | |||
1127.1.f | \(\chi_{1127}(275, \cdot)\) | 1127.1.f.a | 2 | 2 |
1127.1.f.b | 2 | |||
1127.1.f.c | 2 | |||
1127.1.f.d | 4 | |||
1127.1.f.e | 4 | |||
1127.1.f.f | 8 | |||
1127.1.h | \(\chi_{1127}(668, \cdot)\) | None | 0 | 2 |
1127.1.k | \(\chi_{1127}(22, \cdot)\) | None | 0 | 6 |
1127.1.m | \(\chi_{1127}(139, \cdot)\) | None | 0 | 6 |
1127.1.o | \(\chi_{1127}(99, \cdot)\) | 1127.1.o.a | 10 | 10 |
1127.1.q | \(\chi_{1127}(48, \cdot)\) | None | 0 | 10 |
1127.1.s | \(\chi_{1127}(24, \cdot)\) | None | 0 | 12 |
1127.1.u | \(\chi_{1127}(114, \cdot)\) | None | 0 | 12 |
1127.1.v | \(\chi_{1127}(31, \cdot)\) | 1127.1.v.a | 20 | 20 |
1127.1.x | \(\chi_{1127}(30, \cdot)\) | 1127.1.x.a | 20 | 20 |
1127.1.z | \(\chi_{1127}(6, \cdot)\) | None | 0 | 60 |
1127.1.bb | \(\chi_{1127}(15, \cdot)\) | None | 0 | 60 |
1127.1.bd | \(\chi_{1127}(11, \cdot)\) | None | 0 | 120 |
1127.1.bf | \(\chi_{1127}(3, \cdot)\) | None | 0 | 120 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1127))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(1127)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)