Defining parameters
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.bf (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 171 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(342, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 120 | 264 |
Cusp forms | 336 | 120 | 216 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(342, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
342.2.bf.a | $12$ | $2.731$ | 12.0.\(\cdots\).1 | None | \(0\) | \(-6\) | \(0\) | \(18\) | \(q+(\beta _{6}-\beta _{10})q^{2}+(-1+\beta _{8})q^{3}-\beta _{7}q^{4}+\cdots\) |
342.2.bf.b | $48$ | $2.731$ | None | \(0\) | \(9\) | \(0\) | \(-18\) | ||
342.2.bf.c | $60$ | $2.731$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(342, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)