Defining parameters
Level: | \( N \) | \(=\) | \( 234 = 2 \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 234.l (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(84\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(234, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 100 | 12 | 88 |
Cusp forms | 68 | 12 | 56 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(234, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
234.2.l.a | $4$ | $1.868$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(-6\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-1+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\) |
234.2.l.b | $4$ | $1.868$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+3\zeta_{12}^{3}q^{5}+\cdots\) |
234.2.l.c | $4$ | $1.868$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(6\) | \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(1-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(234, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)