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Properties

Label 126.3.q
Level $126$
Weight $3$
Character orbit 126.q
Rep. character $\chi_{126}(29,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
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 24 80
Cusp forms 88 24 64
Eisenstein series 16 0 16

Trace form

\( 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} + O(q^{10}) \) \( 24 q + 24 q^{4} + 36 q^{5} + 8 q^{6} - 32 q^{9} - 24 q^{12} - 44 q^{15} - 48 q^{16} + 48 q^{18} + 24 q^{19} + 72 q^{20} + 28 q^{21} + 24 q^{22} - 72 q^{23} - 16 q^{24} + 72 q^{25} - 108 q^{29} - 56 q^{30} - 60 q^{31} + 104 q^{33} - 48 q^{34} - 80 q^{36} - 168 q^{37} + 144 q^{38} + 64 q^{39} + 108 q^{41} + 60 q^{43} + 116 q^{45} - 324 q^{47} - 48 q^{48} - 84 q^{49} + 144 q^{50} - 268 q^{51} - 208 q^{54} + 264 q^{55} + 60 q^{57} - 432 q^{59} - 32 q^{60} - 192 q^{64} - 180 q^{65} - 112 q^{66} + 72 q^{67} + 72 q^{68} + 536 q^{69} + 96 q^{72} + 24 q^{73} + 288 q^{74} + 76 q^{75} + 24 q^{76} - 64 q^{78} + 12 q^{79} + 544 q^{81} - 288 q^{82} + 756 q^{83} + 112 q^{84} - 156 q^{85} + 360 q^{86} + 280 q^{87} - 48 q^{88} + 80 q^{90} - 168 q^{91} - 144 q^{92} + 436 q^{93} - 936 q^{95} - 64 q^{96} + 48 q^{97} - 440 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.3.q.a 126.q 9.d $24$ $3.433$ None \(0\) \(0\) \(36\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

\( S_{3}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)