Defining parameters
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.bg (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 152 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(80\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(608, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 18 | 54 |
Cusp forms | 24 | 6 | 18 |
Eisenstein series | 48 | 12 | 36 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 6 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(608, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
608.1.bg.a | $6$ | $0.303$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(3\) | \(0\) | \(0\) | \(q+(\zeta_{18}-\zeta_{18}^{6})q^{3}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(608, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(608, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)