Defining parameters
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(1568, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 44 | 4 | 40 |
Cusp forms | 12 | 4 | 8 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 0 | 4 | 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.d.a | $2$ | $0.783$ | \(\Q(\sqrt{-1}) \) | $A_{4}$ | None | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q-iq^{3}-q^{5}-iq^{11}+iq^{15}-q^{17}+\cdots\) |
1568.1.d.b | $2$ | $0.783$ | \(\Q(\sqrt{-1}) \) | $A_{4}$ | None | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-iq^{3}+q^{5}+iq^{11}-iq^{15}+q^{17}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(1568, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(1568, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)