Defining parameters
Level: | \( N \) | = | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | = | \( 14 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(1120\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(33))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 540 | 394 | 146 |
Cusp forms | 500 | 374 | 126 |
Eisenstein series | 40 | 20 | 20 |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(33))\)
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 |
---|---|---|---|---|
33.14.a | \(\chi_{33}(1, \cdot)\) | 33.14.a.a | 1 | 1 |
33.14.a.b | 4 | |||
33.14.a.c | 4 | |||
33.14.a.d | 5 | |||
33.14.a.e | 6 | |||
33.14.d | \(\chi_{33}(32, \cdot)\) | 33.14.d.a | 2 | 1 |
33.14.d.b | 48 | |||
33.14.e | \(\chi_{33}(4, \cdot)\) | n/a | 104 | 4 |
33.14.f | \(\chi_{33}(2, \cdot)\) | n/a | 200 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(33))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_1(33)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)