Defining parameters
| Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 840.u (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 840 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(15\) | ||
| Distinguishing \(T_p\): | \(11\), \(23\), \(73\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 200 | 200 | 0 |
| Cusp forms | 184 | 184 | 0 |
| Eisenstein series | 16 | 16 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(840, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 840.2.u.a | $4$ | $6.707$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-\beta _{1}q^{2}-\beta _{2}q^{3}-2q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
| 840.2.u.b | $4$ | $6.707$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | \(\Q(\sqrt{-6}) \) | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-2q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) |
| 840.2.u.c | $8$ | $6.707$ | 8.0.2517630976.5 | \(\Q(\sqrt{-14}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}-\beta _{6}q^{5}+(\beta _{3}+\cdots)q^{6}+\cdots\) |
| 840.2.u.d | $8$ | $6.707$ | 8.0.2517630976.5 | \(\Q(\sqrt{-14}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+2q^{4}+\beta _{6}q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots\) |
| 840.2.u.e | $160$ | $6.707$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||