Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.g (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 90 | 4 | 86 |
Cusp forms | 54 | 4 | 50 |
Eisenstein series | 36 | 0 | 36 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(108, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
108.3.g.a | $4$ | $2.943$ | \(\Q(\sqrt{-3}, \sqrt{-11})\) | None | \(0\) | \(0\) | \(-9\) | \(-1\) | \(q+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\beta _{1}-2\beta _{3})q^{7}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(108, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)