Defining parameters
| Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 1 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2240.bt (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 3 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(2240, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 88 | 16 | 72 |
| Cusp forms | 40 | 8 | 32 |
| Eisenstein series | 48 | 8 | 40 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 8 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(2240, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | Image | CM | RM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||||
| 2240.1.bt.a | $2$ | $1.118$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(-1\) | \(1\) | \(-1\) | \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}-q^{15}+\cdots\) |
| 2240.1.bt.b | $2$ | $1.118$ | \(\Q(\sqrt{-3}) \) | $D_{3}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(q-\zeta_{6}^{2}q^{3}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{15}+\cdots\) |
| 2240.1.bt.c | $4$ | $1.118$ | \(\Q(\zeta_{12})\) | $D_{6}$ | \(\Q(\sqrt{-5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{5}q^{7}+\cdots\) |
Decomposition of \(S_{1}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces
\( S_{1}^{\mathrm{old}}(2240, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)