Defining parameters
| Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 420.f (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(384\) | ||
| Trace bound: | \(1\) | ||
| Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(420, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 300 | 48 | 252 |
| Cusp forms | 276 | 48 | 228 |
| Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(420, [\chi])\) into newform subspaces
| Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
| 420.4.f.a | $8$ | $24.781$ | \(\Q(\sqrt{-3}, \sqrt{-5}, \sqrt{7})\) | \(\Q(\sqrt{-35}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{3}-5\beta _{1}q^{5}+7\beta _{3}q^{7}+\cdots\) |
| 420.4.f.b | $40$ | $24.781$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
Decomposition of \(S_{4}^{\mathrm{old}}(420, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(420, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)