Defining parameters
Level: | \( N \) | \(=\) | \( 342 = 2 \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 342.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 18 | 110 |
Cusp forms | 112 | 18 | 94 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
342.3.d.a | $2$ | $9.319$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(2\) | \(10\) | \(q-\beta q^{2}-2q^{4}+q^{5}+5q^{7}+2\beta q^{8}+\cdots\) |
342.3.d.b | $8$ | $9.319$ | 8.0.\(\cdots\).3 | None | \(0\) | \(0\) | \(-4\) | \(-12\) | \(q+\beta _{2}q^{2}-2q^{4}-\beta _{5}q^{5}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\) |
342.3.d.c | $8$ | $9.319$ | 8.0.\(\cdots\).9 | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q-\beta _{3}q^{2}-2q^{4}-\beta _{1}q^{5}+(1+\beta _{6})q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)