Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(36\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 2 | 52 |
Cusp forms | 18 | 2 | 16 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.2.e.a | $2$ | $0.862$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(3\) | \(1\) | \(q+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)