Defining parameters
Level: | \( N \) | \(=\) | \( 861 = 3 \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 861.s (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(12\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(861, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 232 | 212 | 20 |
Cusp forms | 216 | 212 | 4 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(861, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
861.2.s.a | $106$ | $6.875$ | None | \(0\) | \(0\) | \(0\) | \(-5\) | ||
861.2.s.b | $106$ | $6.875$ | None | \(0\) | \(0\) | \(0\) | \(-5\) |
Decomposition of \(S_{2}^{\mathrm{old}}(861, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(861, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)