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Properties

Label 108.9.f
Level $108$
Weight $9$
Character orbit 108.f
Rep. character $\chi_{108}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $1$
Sturm bound $162$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(162\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(108, [\chi])\).

Total New Old
Modular forms 300 100 200
Cusp forms 276 92 184
Eisenstein series 24 8 16

Trace form

\( 92 q + q^{2} - q^{4} + 2 q^{5} + 9958 q^{8} + 508 q^{10} - 2 q^{13} + 9348 q^{14} - q^{16} - 27544 q^{17} - 26260 q^{20} - 513 q^{22} - 2968752 q^{25} + 2625752 q^{26} - 131076 q^{28} + 632546 q^{29}+ \cdots + 17303818 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.9.f.a 108.f 36.f $92$ $43.997$ None 36.9.f.a \(1\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{9}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(108, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)