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Properties

Label 342.3.o
Level $342$
Weight $3$
Character orbit 342.o
Rep. character $\chi_{342}(77,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 342.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(342, [\chi])\).

Total New Old
Modular forms 248 72 176
Cusp forms 232 72 160
Eisenstein series 16 0 16

Trace form

\( 72 q + 4 q^{3} + 72 q^{4} + 36 q^{5} + 16 q^{6} - 20 q^{9} + O(q^{10}) \) \( 72 q + 4 q^{3} + 72 q^{4} + 36 q^{5} + 16 q^{6} - 20 q^{9} - 72 q^{11} - 8 q^{12} - 72 q^{14} - 80 q^{15} - 144 q^{16} - 16 q^{18} + 72 q^{20} - 36 q^{21} + 108 q^{23} + 16 q^{24} + 192 q^{25} - 20 q^{27} + 72 q^{29} - 56 q^{30} - 60 q^{31} - 124 q^{33} - 32 q^{36} - 168 q^{37} + 36 q^{39} + 144 q^{41} + 8 q^{42} + 104 q^{45} + 48 q^{46} - 36 q^{47} - 32 q^{48} - 204 q^{49} + 424 q^{51} + 40 q^{54} + 216 q^{55} - 144 q^{56} - 48 q^{58} - 180 q^{59} - 8 q^{60} - 96 q^{61} - 272 q^{63} - 576 q^{64} + 108 q^{65} + 96 q^{66} + 156 q^{67} - 232 q^{69} + 216 q^{70} + 32 q^{72} - 216 q^{74} + 168 q^{75} - 684 q^{77} + 16 q^{78} - 96 q^{79} + 580 q^{81} - 96 q^{82} + 288 q^{83} + 168 q^{84} - 216 q^{85} - 288 q^{86} + 104 q^{87} + 512 q^{90} - 336 q^{91} + 216 q^{92} - 116 q^{93} - 168 q^{94} - 32 q^{96} - 12 q^{97} - 464 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(342, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.3.o.a 342.o 9.d $72$ $9.319$ None \(0\) \(4\) \(36\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(342, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(342, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)