Defining parameters
Level: | \( N \) | \(=\) | \( 2624 = 2^{6} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2624.dr (of order \(40\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 328 \) |
Character field: | \(\Q(\zeta_{40})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(336\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2624, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 224 | 32 | 192 |
Cusp forms | 32 | 32 | 0 |
Eisenstein series | 192 | 0 | 192 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 32 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2624, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
2624.1.dr.a | $16$ | $1.310$ | \(\Q(\zeta_{40})\) | $D_{40}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{40}+\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\) |
2624.1.dr.b | $16$ | $1.310$ | \(\Q(\zeta_{40})\) | $D_{40}$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{40}-\zeta_{40}^{14})q^{3}+(\zeta_{40}^{2}-\zeta_{40}^{8}+\cdots)q^{9}+\cdots\) |