Defining parameters
| Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(768\) | ||
| Trace bound: | \(7\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 1200 | 96 | 1104 |
| Cusp forms | 1104 | 96 | 1008 |
| Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 1008.4.bt.a | \(16\) | \(59.474\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-56\) | \(q-\beta _{13}q^{5}+(-3+\beta _{4})q^{7}+(-\beta _{1}-3\beta _{6}+\cdots)q^{11}+\cdots\) |
| 1008.4.bt.b | \(16\) | \(59.474\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{9}q^{5}+(-1-2\beta _{1}+\beta _{6}+\beta _{8})q^{7}+\cdots\) |
| 1008.4.bt.c | \(16\) | \(59.474\) | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(64\) | \(q+(-\beta _{10}+\beta _{12})q^{5}+(6-3\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\) |
| 1008.4.bt.d | \(48\) | \(59.474\) | None | \(0\) | \(0\) | \(0\) | \(24\) | ||
Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)