Defining parameters
Level: | \( N \) | \(=\) | \( 3311 = 7 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3311.gd (of order \(210\) and degree \(48\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3311 \) |
Character field: | \(\Q(\zeta_{210})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(352\) | ||
Trace bound: | \(8\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3311, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 288 | 288 | 0 |
Cusp forms | 96 | 96 | 0 |
Eisenstein series | 192 | 192 | 0 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 96 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3311, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3311.1.gd.a | $48$ | $1.652$ | \(\Q(\zeta_{210})\) | $D_{105}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(6\) | \(q+(\zeta_{210}^{2}+\zeta_{210}^{34})q^{2}+(\zeta_{210}^{4}+\zeta_{210}^{36}+\cdots)q^{4}+\cdots\) |
3311.1.gd.b | $48$ | $1.652$ | \(\Q(\zeta_{210})\) | $D_{105}$ | \(\Q(\sqrt{-7}) \) | None | \(-2\) | \(0\) | \(0\) | \(6\) | \(q+(\zeta_{210}^{44}-\zeta_{210}^{97})q^{2}+(\zeta_{210}^{36}+\zeta_{210}^{88}+\cdots)q^{4}+\cdots\) |