Defining parameters
| Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 840.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(840, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 208 | 32 | 176 |
| Cusp forms | 176 | 32 | 144 |
| Eisenstein series | 32 | 0 | 32 |
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.f.a | $16$ | $6.707$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(-16\) | \(2\) | \(q+\beta _{2}q^{3}-q^{5}+\beta _{4}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\) |
| 840.2.f.b | $16$ | $6.707$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(16\) | \(2\) | \(q-\beta _{2}q^{3}+q^{5}+\beta _{9}q^{7}-\beta _{1}q^{9}+\beta _{8}q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(840, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(840, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)