Defining parameters
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.z (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(256\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1344, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 12 | 52 |
Cusp forms | 16 | 4 | 12 |
Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1344.1.z.a | $2$ | $0.671$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(0\) | \(-1\) | \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\) |
1344.1.z.b | $2$ | $0.671$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(1\) | \(0\) | \(1\) | \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1344, [\chi]) \cong \)