Defining parameters
Level: | \( N \) | = | \( 968 = 2^{3} \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 9 \) | ||
Sturm bound: | \(58080\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(968))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1076 | 357 | 719 |
Cusp forms | 116 | 76 | 40 |
Eisenstein series | 960 | 281 | 679 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 66 | 0 | 10 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(968))\)
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 |
---|---|---|---|---|
968.1.b | \(\chi_{968}(725, \cdot)\) | None | 0 | 1 |
968.1.d | \(\chi_{968}(727, \cdot)\) | None | 0 | 1 |
968.1.f | \(\chi_{968}(243, \cdot)\) | 968.1.f.a | 2 | 1 |
968.1.f.b | 2 | |||
968.1.h | \(\chi_{968}(241, \cdot)\) | 968.1.h.a | 2 | 1 |
968.1.j | \(\chi_{968}(161, \cdot)\) | 968.1.j.a | 8 | 4 |
968.1.l | \(\chi_{968}(3, \cdot)\) | 968.1.l.a | 4 | 4 |
968.1.l.b | 4 | |||
968.1.l.c | 4 | |||
968.1.n | \(\chi_{968}(487, \cdot)\) | None | 0 | 4 |
968.1.p | \(\chi_{968}(645, \cdot)\) | None | 0 | 4 |
968.1.s | \(\chi_{968}(23, \cdot)\) | None | 0 | 10 |
968.1.u | \(\chi_{968}(21, \cdot)\) | None | 0 | 10 |
968.1.v | \(\chi_{968}(65, \cdot)\) | None | 0 | 10 |
968.1.x | \(\chi_{968}(67, \cdot)\) | 968.1.x.a | 10 | 10 |
968.1.z | \(\chi_{968}(59, \cdot)\) | 968.1.z.a | 40 | 40 |
968.1.bb | \(\chi_{968}(17, \cdot)\) | None | 0 | 40 |
968.1.bc | \(\chi_{968}(13, \cdot)\) | None | 0 | 40 |
968.1.be | \(\chi_{968}(15, \cdot)\) | None | 0 | 40 |
Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(968))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(968)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)