Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(27\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(81, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 10 | 14 |
Cusp forms | 12 | 6 | 6 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(81, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
81.3.b.a | $2$ | $2.207$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(0\) | \(0\) | \(4\) | \(q-\zeta_{6}q^{2}+q^{4}-2\zeta_{6}q^{5}+2q^{7}-5\zeta_{6}q^{8}+\cdots\) |
81.3.b.b | $4$ | $2.207$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(81, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(81, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)