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Properties

Label 124.4.g
Level $124$
Weight $4$
Character orbit 124.g
Rep. character $\chi_{124}(99,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 124.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 124 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(124, [\chi])\).

Total New Old
Modular forms 100 100 0
Cusp forms 92 92 0
Eisenstein series 8 8 0

Trace form

\( 92 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 6 q^{6} + 32 q^{8} - 380 q^{9} + O(q^{10}) \) \( 92 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 6 q^{6} + 32 q^{8} - 380 q^{9} + 24 q^{10} + 78 q^{12} + 102 q^{13} - 130 q^{14} + 72 q^{16} - 6 q^{17} + 138 q^{18} - 322 q^{20} - 6 q^{21} + 216 q^{22} + 78 q^{24} - 784 q^{25} - 12 q^{26} + 222 q^{28} + 596 q^{32} + 124 q^{33} - 444 q^{34} - 160 q^{36} - 762 q^{37} - 48 q^{38} + 102 q^{40} - 2 q^{41} + 1116 q^{42} + 1038 q^{44} - 48 q^{45} + 408 q^{48} + 788 q^{49} + 188 q^{50} + 24 q^{52} - 30 q^{53} - 1186 q^{56} - 762 q^{57} + 1228 q^{62} - 4384 q^{64} - 6 q^{65} - 1272 q^{66} + 4692 q^{68} + 1148 q^{69} - 2184 q^{70} + 1422 q^{72} + 966 q^{73} + 2142 q^{74} - 88 q^{76} + 4316 q^{78} + 550 q^{80} - 2486 q^{81} + 2706 q^{82} - 5700 q^{84} - 3150 q^{86} + 1320 q^{88} + 2206 q^{90} - 3510 q^{93} - 7212 q^{94} + 4170 q^{96} + 1824 q^{97} - 2806 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(124, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
124.4.g.a 124.g 124.g $92$ $7.316$ None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$