Defining parameters
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.ft (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 840 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(768\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(3360, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 192 | 48 | 144 |
Cusp forms | 64 | 16 | 48 |
Eisenstein series | 128 | 32 | 96 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 16 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
3360.1.ft.a | $8$ | $1.677$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\zeta_{24}^{5}q^{3}-\zeta_{24}^{11}q^{5}+\zeta_{24}^{8}q^{7}+\cdots\) |
3360.1.ft.b | $8$ | $1.677$ | \(\Q(\zeta_{24})\) | $D_{12}$ | \(\Q(\sqrt{-6}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{3}+\zeta_{24}^{3}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 3}\)