Defining parameters
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(54\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(108, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 42 | 16 | 26 |
Cusp forms | 30 | 16 | 14 |
Eisenstein series | 12 | 0 | 12 |
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.d.a | $2$ | $2.943$ | \(\Q(\sqrt{-3}) \) | None | \(-2\) | \(0\) | \(14\) | \(0\) | \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}+7q^{5}+\cdots\) |
108.3.d.b | $2$ | $2.943$ | \(\Q(\sqrt{-3}) \) | None | \(2\) | \(0\) | \(-14\) | \(0\) | \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{4}-7q^{5}+\cdots\) |
108.3.d.c | $4$ | $2.943$ | \(\Q(\sqrt{-3}, \sqrt{13})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{1}-\beta _{2})q^{2}+(3+\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\) |
108.3.d.d | $8$ | $2.943$ | 8.0.207360000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-1+\beta _{5})q^{4}+(-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(108, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)