Defining parameters
Level: | \( N \) | = | \( 3 \) |
Weight: | \( k \) | = | \( 42 \) |
Nonzero newspaces: | \( 1 \) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 7 | 8 |
Cusp forms | 13 | 7 | 6 |
Eisenstein series | 2 | 0 | 2 |
Trace form
Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(3))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
3.42.a | \(\chi_{3}(1, \cdot)\) | 3.42.a.a | 3 | 1 |
3.42.a.b | 4 |
Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces
\( S_{42}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)