Properties

Label 9.8.c
Level $9$
Weight $8$
Character orbit 9.c
Rep. character $\chi_{9}(4,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 9 = 3^{2} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 9.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(9, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 12 12 0
Eisenstein series 4 4 0

Trace form

\( 12 q - 9 q^{2} + 24 q^{3} - 321 q^{4} - 180 q^{5} - 1233 q^{6} - 84 q^{7} + 5922 q^{8} + 990 q^{9} + 252 q^{10} - 8460 q^{11} + 8052 q^{12} - 1848 q^{13} - 16272 q^{14} - 1188 q^{15} - 12417 q^{16} + 30564 q^{17}+ \cdots - 49382676 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(9, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
9.8.c.a 9.c 9.c $12$ $2.811$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 9.8.c.a \(-9\) \(24\) \(-180\) \(-84\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)