Defining parameters
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.l (of order \(14\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 147 \) |
Character field: | \(\Q(\zeta_{14})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(18\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(147, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 18 | 18 | 0 |
Cusp forms | 6 | 6 | 0 |
Eisenstein series | 12 | 12 | 0 |
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 \(S_{1}^{\mathrm{new}}(147, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
147.1.l.a | $6$ | $0.073$ | \(\Q(\zeta_{14})\) | $D_{7}$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-1\) | \(0\) | \(-1\) | \(q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots\) |