Properties

Label 108.4.l
Level $108$
Weight $4$
Character orbit 108.l
Rep. character $\chi_{108}(11,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $312$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 108 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(108, [\chi])\).

Total New Old
Modular forms 336 336 0
Cusp forms 312 312 0
Eisenstein series 24 24 0

Trace form

\( 312 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 123 q^{12} - 12 q^{13} + 69 q^{14} - 6 q^{16} - 18 q^{17} + 351 q^{18} + 225 q^{20} - 12 q^{21} - 6 q^{22} - 300 q^{24} - 12 q^{25}+ \cdots + 2898 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
108.4.l.a 108.l 108.l $312$ $6.372$ None 108.4.l.a \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$