Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 36 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
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 | 192 | 64 | 128 |
Cusp forms | 168 | 56 | 112 |
Eisenstein series | 24 | 8 | 16 |
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.h.a | $56$ | $17.321$ | None | \(3\) | \(0\) | \(6\) | \(0\) |
Decomposition of \(S_{6}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)