Defining parameters
Level: | \( N \) | = | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 3 \) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(486\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(54))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 192 | 42 | 150 |
Cusp forms | 132 | 42 | 90 |
Eisenstein series | 60 | 0 | 60 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)
We only show spaces with odd 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 |
---|---|---|---|---|
54.3.b | \(\chi_{54}(53, \cdot)\) | 54.3.b.a | 2 | 1 |
54.3.d | \(\chi_{54}(17, \cdot)\) | 54.3.d.a | 4 | 2 |
54.3.f | \(\chi_{54}(5, \cdot)\) | 54.3.f.a | 36 | 6 |
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)