Defining parameters
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.ci (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 936 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3744, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 80 | 20 | 60 |
Cusp forms | 48 | 12 | 36 |
Eisenstein series | 32 | 8 | 24 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 12 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3744.1.ci.a | $6$ | $1.868$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-26}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{18}^{2}q^{3}+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{5}+(\zeta_{18}^{7}+\cdots)q^{7}+\cdots\) |
3744.1.ci.b | $6$ | $1.868$ | \(\Q(\zeta_{18})\) | $D_{9}$ | \(\Q(\sqrt{-26}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{18}^{5}q^{3}+(\zeta_{18}-\zeta_{18}^{2})q^{5}+(\zeta_{18}^{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3744, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)