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Properties

Label 342.3.y
Level $342$
Weight $3$
Character orbit 342.y
Rep. character $\chi_{342}(5,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $240$
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.y (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{18})\)
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 744 240 504
Cusp forms 696 240 456
Eisenstein series 48 0 48

Trace form

\( 240 q - 12 q^{3} + 24 q^{6} - 12 q^{9} + O(q^{10}) \) \( 240 q - 12 q^{3} + 24 q^{6} - 12 q^{9} - 30 q^{13} + 60 q^{15} + 162 q^{17} + 48 q^{18} + 42 q^{19} - 36 q^{22} - 216 q^{23} + 24 q^{24} + 30 q^{27} - 12 q^{28} - 192 q^{33} + 24 q^{36} + 60 q^{39} - 48 q^{43} + 252 q^{45} + 24 q^{48} - 840 q^{49} + 66 q^{51} - 120 q^{52} - 144 q^{54} + 204 q^{57} - 270 q^{59} - 12 q^{60} + 42 q^{61} - 240 q^{63} + 960 q^{64} - 24 q^{66} + 168 q^{67} - 108 q^{68} - 468 q^{69} - 48 q^{72} + 258 q^{73} + 744 q^{78} + 204 q^{79} - 1212 q^{81} - 144 q^{82} - 216 q^{83} + 180 q^{84} + 708 q^{87} + 648 q^{89} - 24 q^{90} - 192 q^{91} - 480 q^{93} + 648 q^{95} + 180 q^{97} - 648 q^{98} + 1266 q^{99} + O(q^{100}) \)

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.y.a 342.y 171.z $240$ $9.319$ None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

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

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