Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
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: | \(108\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 198 | 10 | 188 |
Cusp forms | 162 | 10 | 152 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.6.e.a | $10$ | $17.321$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(21\) | \(29\) | \(q+(4-4\beta _{1}+\beta _{7})q^{5}+(6\beta _{1}+\beta _{2}+\beta _{7}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(108, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)