Defining parameters
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.g (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 63 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 60 | 20 | 40 |
Cusp forms | 36 | 12 | 24 |
Eisenstein series | 24 | 8 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
189.2.g.a | $2$ | $1.509$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(0\) | \(2\) | \(1\) | \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\) |
189.2.g.b | $10$ | $1.509$ | 10.0.\(\cdots\).1 | None | \(-2\) | \(0\) | \(8\) | \(-1\) | \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)