Defining parameters
| Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\) and degree \(2\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
| Character field: | \(\Q(\zeta_{6})\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(576\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 608 | 48 | 560 |
| Cusp forms | 544 | 48 | 496 |
| Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 1386.2.r.a | \(8\) | \(11.067\) | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(-8\) | \(0\) | \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-2+\zeta_{24}+\cdots)q^{5}+\cdots\) |
| 1386.2.r.b | \(8\) | \(11.067\) | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\) |
| 1386.2.r.c | \(8\) | \(11.067\) | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(8\) | \(0\) | \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(2+\zeta_{24}-2\zeta_{24}^{4}+\cdots)q^{5}+\cdots\) |
| 1386.2.r.d | \(24\) | \(11.067\) | None | \(0\) | \(0\) | \(0\) | \(8\) | ||
Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)