Defining parameters
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.u (of order \(33\) and degree \(20\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 847 \) |
Character field: | \(\Q(\zeta_{33})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(176\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1800 | 1800 | 0 |
Cusp forms | 1720 | 1720 | 0 |
Eisenstein series | 80 | 80 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
847.2.u.a | $1720$ | $6.763$ | None | \(-11\) | \(-20\) | \(-7\) | \(-24\) |