Defining parameters
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.dp (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 420 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1680, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 8 | 72 |
Cusp forms | 32 | 8 | 24 |
Eisenstein series | 48 | 0 | 48 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1680, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1680.1.dp.a | $2$ | $0.838$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(-2\) | \(-1\) | \(-1\) | \(q-q^{3}-\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+q^{9}+\zeta_{6}q^{15}+\cdots\) |
1680.1.dp.b | $2$ | $0.838$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(-1\) | \(1\) | \(-1\) | \(q-\zeta_{6}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
1680.1.dp.c | $2$ | $0.838$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(q+\zeta_{6}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\cdots\) |
1680.1.dp.d | $2$ | $0.838$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(2\) | \(-1\) | \(1\) | \(q+q^{3}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{9}-\zeta_{6}q^{15}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)