Defining parameters
| Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1344.o (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 84 \) |
| Character field: | \(\Q\) | ||
| 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 | 32 | 6 | 26 |
| Cusp forms | 8 | 2 | 6 |
| Eisenstein series | 24 | 4 | 20 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 2 | 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.o.a | $1$ | $0.671$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) | \(\Q(\sqrt{7}) \) | \(0\) | \(-1\) | \(0\) | \(-1\) | \(q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots\) |
| 1344.1.o.b | $1$ | $0.671$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) | \(\Q(\sqrt{7}) \) | \(0\) | \(1\) | \(0\) | \(1\) | \(q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)