Defining parameters
Level: | \( N \) | = | \( 129 = 3 \cdot 43 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(1232\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(129))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 90 | 46 | 44 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 84 | 40 | 44 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(129))\)
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 |
---|---|---|---|---|
129.1.b | \(\chi_{129}(85, \cdot)\) | None | 0 | 1 |
129.1.c | \(\chi_{129}(44, \cdot)\) | None | 0 | 1 |
129.1.f | \(\chi_{129}(92, \cdot)\) | None | 0 | 2 |
129.1.g | \(\chi_{129}(7, \cdot)\) | None | 0 | 2 |
129.1.k | \(\chi_{129}(22, \cdot)\) | None | 0 | 6 |
129.1.l | \(\chi_{129}(11, \cdot)\) | 129.1.l.a | 6 | 6 |
129.1.o | \(\chi_{129}(14, \cdot)\) | None | 0 | 12 |
129.1.p | \(\chi_{129}(19, \cdot)\) | None | 0 | 12 |