Defining parameters
Level: | \( N \) | \(=\) | \( 2144 = 2^{5} \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2144.bu (of order \(66\) and degree \(20\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 536 \) |
Character field: | \(\Q(\zeta_{66})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(272\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 240 | 60 | 180 |
Cusp forms | 80 | 20 | 60 |
Eisenstein series | 160 | 40 | 120 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 20 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2144, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2144.1.bu.a | $20$ | $1.070$ | \(\Q(\zeta_{33})\) | $D_{33}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q+(-\zeta_{66}^{8}+\zeta_{66}^{13})q^{3}+(\zeta_{66}^{16}-\zeta_{66}^{21}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2144, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2144, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(536, [\chi])\)\(^{\oplus 3}\)