Defining parameters
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(81\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(162, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 16 | 116 |
Cusp forms | 84 | 16 | 68 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(162, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
162.3.d.a | $4$ | $4.414$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(-10\) | \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(-6\beta _{1}+6\beta _{3})q^{5}+\cdots\) |
162.3.d.b | $4$ | $4.414$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(3\beta _{1}-3\beta _{3})q^{5}+\cdots\) |
162.3.d.c | $8$ | $4.414$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\zeta_{24}^{5}q^{2}+2\zeta_{24}q^{4}+(2\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(162, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(162, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)