Defining parameters
Level: | \( N \) | \(=\) | \( 3248 = 2^{4} \cdot 7 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3248.ei (of order \(28\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3248 \) |
Character field: | \(\Q(\zeta_{28})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3248, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 72 | 0 |
Cusp forms | 24 | 24 | 0 |
Eisenstein series | 48 | 48 | 0 |
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 \(S_{1}^{\mathrm{new}}(3248, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3248.1.ei.a | $12$ | $1.621$ | \(\Q(\zeta_{28})\) | $D_{28}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{28}^{5}q^{2}+\zeta_{28}^{10}q^{4}-\zeta_{28}^{13}q^{7}+\cdots\) |
3248.1.ei.b | $12$ | $1.621$ | \(\Q(\zeta_{28})\) | $D_{28}$ | \(\Q(\sqrt{-7}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}-\zeta_{28}^{13}q^{7}+\cdots\) |