Defining parameters
Level: | \( N \) | = | \( 166 = 2 \cdot 83 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(3444\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(166))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 943 | 286 | 657 |
Cusp forms | 780 | 286 | 494 |
Eisenstein series | 163 | 0 | 163 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)
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 available newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
166.2.a | \(\chi_{166}(1, \cdot)\) | 166.2.a.a | 1 | 1 |
166.2.a.b | 2 | |||
166.2.a.c | 3 | |||
166.2.c | \(\chi_{166}(3, \cdot)\) | 166.2.c.a | 120 | 40 |
166.2.c.b | 160 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(166))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(166)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 2}\)