Defining parameters
Level: | \( N \) | = | \( 9 = 3^{2} \) |
Weight: | \( k \) | = | \( 42 \) |
Nonzero newspaces: | \( 2 \) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(252\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_1(9))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 127 | 101 | 26 |
Cusp forms | 119 | 96 | 23 |
Eisenstein series | 8 | 5 | 3 |
Trace form
Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_1(9))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
9.42.a | \(\chi_{9}(1, \cdot)\) | 9.42.a.a | 3 | 1 |
9.42.a.b | 3 | |||
9.42.a.c | 4 | |||
9.42.a.d | 6 | |||
9.42.c | \(\chi_{9}(4, \cdot)\) | 9.42.c.a | 80 | 2 |
Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces
\( S_{42}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{42}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)