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Properties

Label 104.4.r
Level $104$
Weight $4$
Character orbit 104.r
Rep. character $\chi_{104}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 104.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(104, [\chi])\).

Total New Old
Modular forms 88 88 0
Cusp forms 80 80 0
Eisenstein series 8 8 0

Trace form

\( 80 q - q^{2} - q^{4} - 2 q^{6} - 2 q^{7} - 10 q^{8} + 322 q^{9} + 43 q^{10} + 44 q^{12} - 92 q^{14} + 52 q^{15} - 65 q^{16} - 28 q^{17} + 330 q^{18} + 233 q^{20} + 152 q^{22} + 274 q^{23} + 390 q^{24}+ \cdots + 3677 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(104, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.4.r.a 104.r 104.r $80$ $6.136$ None 104.4.r.a \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$