Defining parameters
Level: | \( N \) | \(=\) | \( 3479 = 7^{2} \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3479.ea (of order \(70\) and degree \(24\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 71 \) |
Character field: | \(\Q(\zeta_{70})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3479, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 144 | 72 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 192 | 120 | 72 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 24 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3479, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3479.1.ea.a | $24$ | $1.736$ | \(\Q(\zeta_{35})\) | $D_{70}$ | \(\Q(\sqrt{-7}) \) | None | \(-3\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{70}^{10}-\zeta_{70}^{27})q^{2}+(\zeta_{70}^{2}-\zeta_{70}^{19}+\cdots)q^{4}+\cdots\) |