Defining parameters
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 231 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(693, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20 | 4 | 16 |
Cusp forms | 12 | 4 | 8 |
Eisenstein series | 8 | 0 | 8 |
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 \(S_{1}^{\mathrm{new}}(693, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
693.1.h.a | $4$ | $0.346$ | \(\Q(\zeta_{8})\) | $D_{4}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(693, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(693, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)