Defining parameters
Level: | \( N \) | \(=\) | \( 81 = 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 81.d (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(45\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(81, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 34 | 50 |
Cusp forms | 60 | 30 | 30 |
Eisenstein series | 24 | 4 | 20 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(81, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
81.5.d.a | $2$ | $8.373$ | \(\Q(\sqrt{-3}) \) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(-71\) | \(q-2^{4}\zeta_{6}q^{4}+(-71+71\zeta_{6})q^{7}+337\zeta_{6}q^{13}+\cdots\) |
81.5.d.b | $4$ | $8.373$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(38\) | \(q+\beta_1 q^{2}-7\beta_{2} q^{4}+(11\beta_{3}-11\beta_1)q^{5}+\cdots\) |
81.5.d.c | $4$ | $8.373$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(56\) | \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(7\beta _{1}-7\beta _{3})q^{5}+\cdots\) |
81.5.d.d | $4$ | $8.373$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(0\) | \(0\) | \(-34\) | \(q+\beta _{3}q^{2}+(38+38\beta _{1})q^{4}+(2\beta _{2}-2\beta _{3})q^{5}+\cdots\) |
81.5.d.e | $16$ | $8.373$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-52\) | \(q-\beta _{7}q^{2}+(8-8\beta _{1}-\beta _{4}-\beta _{9})q^{4}+\cdots\) |
Decomposition of \(S_{5}^{\mathrm{old}}(81, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)