Defining parameters
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.bb (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 148 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(76\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(592, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 2 | 12 |
Cusp forms | 2 | 2 | 0 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 2 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(592, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
592.1.bb.a | $2$ | $0.295$ | \(\Q(\sqrt{-3}) \) | $D_{6}$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(3\) | \(0\) | \(q+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+(-1+\zeta_{6}^{2}+\cdots)q^{17}+\cdots\) |