Defining parameters
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 8 | 36 |
Cusp forms | 12 | 3 | 9 |
Eisenstein series | 32 | 5 | 27 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 3 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(1568, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
1568.1.g.a | $1$ | $0.783$ | \(\Q\) | $D_{2}$ | \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{14}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-q^{9}+2q^{11}+q^{25}+2q^{43}-2q^{67}+\cdots\) |
1568.1.g.b | $2$ | $0.783$ | \(\Q(\sqrt{2}) \) | $D_{4}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{3}+q^{9}-\beta q^{17}+\beta q^{19}+q^{25}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)