Defining parameters
Level: | \( N \) | \(=\) | \( 806 = 2 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 806.n (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(806, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 232 | 72 | 160 |
Cusp forms | 216 | 72 | 144 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(806, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
806.2.n.a | $28$ | $6.436$ | None | \(0\) | \(6\) | \(0\) | \(0\) | ||
806.2.n.b | $44$ | $6.436$ | None | \(0\) | \(-6\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(806, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(806, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(403, [\chi])\)\(^{\oplus 2}\)