Properties

Label 81.10.e
Level $81$
Weight $10$
Character orbit 81.e
Rep. character $\chi_{81}(10,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $156$
Newform subspaces $1$
Sturm bound $90$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 81 = 3^{4} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 81.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 27 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 1 \)
Sturm bound: \(90\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(81, [\chi])\).

Total New Old
Modular forms 504 168 336
Cusp forms 468 156 312
Eisenstein series 36 12 24

Trace form

\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(81, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
81.10.e.a 81.e 27.e $156$ $41.718$ None 27.10.e.a \(6\) \(0\) \(-2382\) \(-6\) $\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{10}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)