Defining parameters
Level: | \( N \) | = | \( 9 = 3^{2} \) |
Weight: | \( k \) | = | \( 12 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 37 | 29 | 8 |
Cusp forms | 29 | 24 | 5 |
Eisenstein series | 8 | 5 | 3 |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)
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 |
---|---|---|---|---|
9.12.a | \(\chi_{9}(1, \cdot)\) | 9.12.a.a | 1 | 1 |
9.12.a.b | 1 | |||
9.12.a.c | 2 | |||
9.12.c | \(\chi_{9}(4, \cdot)\) | 9.12.c.a | 20 | 2 |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)