Defining parameters
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.l (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(966, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 120 | 280 |
Cusp forms | 368 | 120 | 248 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(966, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
966.2.l.a | $4$ | $7.714$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots\) |
966.2.l.b | $4$ | $7.714$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(6\) | \(0\) | \(-10\) | \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots\) |
966.2.l.c | $56$ | $7.714$ | None | \(0\) | \(-6\) | \(0\) | \(20\) | ||
966.2.l.d | $56$ | $7.714$ | None | \(0\) | \(0\) | \(0\) | \(8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(966, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(966, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(483, [\chi])\)\(^{\oplus 2}\)