Defining parameters
| Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 6 \) | ||
| Sturm bound: | \(256\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(336, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 408 | 100 | 308 |
| Cusp forms | 360 | 92 | 268 |
| Eisenstein series | 48 | 8 | 40 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(336, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 336.4.bc.a | \(2\) | \(19.825\) | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(-9\) | \(0\) | \(-37\) | \(q+(-3-3\zeta_{6})q^{3}+(-18-\zeta_{6})q^{7}+\cdots\) |
| 336.4.bc.b | \(2\) | \(19.825\) | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(9\) | \(0\) | \(17\) | \(q+(3+3\zeta_{6})q^{3}+(18-19\zeta_{6})q^{7}+3^{3}\zeta_{6}q^{9}+\cdots\) |
| 336.4.bc.c | \(12\) | \(19.825\) | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(42\) | \(q+(-\beta _{3}+\beta _{4})q^{3}-\beta _{11}q^{5}+(2-2\beta _{1}+\cdots)q^{7}+\cdots\) |
| 336.4.bc.d | \(12\) | \(19.825\) | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(3\) | \(0\) | \(56\) | \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+(4+2\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\) |
| 336.4.bc.e | \(16\) | \(19.825\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-80\) | \(q-\beta _{4}q^{3}-\beta _{9}q^{5}+(-6-\beta _{1}-2\beta _{2}+\cdots)q^{7}+\cdots\) |
| 336.4.bc.f | \(48\) | \(19.825\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | ||
Decomposition of \(S_{4}^{\mathrm{old}}(336, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)