Properties

Label 126.3.j
Level $126$
Weight $3$
Character orbit 126.j
Rep. character $\chi_{126}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 126.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(126, [\chi])\).

Total New Old
Modular forms 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q - 32 q^{4} - 2 q^{7} - 12 q^{9} + O(q^{10}) \) \( 32 q - 32 q^{4} - 2 q^{7} - 12 q^{9} + 24 q^{11} - 30 q^{13} - 12 q^{14} + 30 q^{15} - 64 q^{16} + 54 q^{17} + 24 q^{18} + 84 q^{23} - 24 q^{24} - 160 q^{25} - 72 q^{26} + 126 q^{27} - 4 q^{28} - 84 q^{29} - 24 q^{31} + 126 q^{33} - 66 q^{35} + 24 q^{36} - 22 q^{37} + 186 q^{39} + 396 q^{41} + 24 q^{42} - 16 q^{43} - 24 q^{44} - 258 q^{45} + 12 q^{46} + 108 q^{47} - 22 q^{49} - 96 q^{50} - 150 q^{51} - 252 q^{53} - 144 q^{54} + 48 q^{56} - 318 q^{57} + 48 q^{58} - 90 q^{59} - 108 q^{60} - 102 q^{61} + 246 q^{63} + 256 q^{64} - 6 q^{65} + 336 q^{66} + 70 q^{67} - 210 q^{69} - 108 q^{70} + 300 q^{71} - 48 q^{72} + 144 q^{74} + 390 q^{75} - 114 q^{77} + 96 q^{78} + 106 q^{79} - 144 q^{81} - 756 q^{83} - 72 q^{84} - 60 q^{85} + 240 q^{86} + 258 q^{87} + 414 q^{89} + 360 q^{90} - 186 q^{91} - 84 q^{92} - 222 q^{93} - 552 q^{95} + 48 q^{96} + 114 q^{97} - 96 q^{98} + 90 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.j.a $32$ $3.433$ None \(0\) \(0\) \(0\) \(-2\)

Decomposition of \(S_{3}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)