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Properties

Label 104.3.x
Level $104$
Weight $3$
Character orbit 104.x
Rep. character $\chi_{104}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $104$
Newform subspaces $1$
Sturm bound $42$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 104.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(42\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(104, [\chi])\).

Total New Old
Modular forms 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 4 q^{2} - 6 q^{4} - 6 q^{6} - 8 q^{7} + 14 q^{8} + 128 q^{9} - 6 q^{10} - 24 q^{14} - 44 q^{15} - 42 q^{16} - 12 q^{17} - 98 q^{18} + 98 q^{20} - 88 q^{22} - 12 q^{23} - 26 q^{24} + 10 q^{26} - 156 q^{28}+ \cdots + 116 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(104, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.3.x.a 104.x 104.x $104$ $2.834$ None 104.3.x.a \(-4\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$