Properties

Label 342.3.t
Level $342$
Weight $3$
Character orbit 342.t
Rep. character $\chi_{342}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
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 80 168
Cusp forms 232 80 152
Eisenstein series 16 0 16

Trace form

\( 80 q - 6 q^{3} + 80 q^{4} - 4 q^{6} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 80 q - 6 q^{3} + 80 q^{4} - 4 q^{6} + 2 q^{7} - 2 q^{9} - 6 q^{11} + 30 q^{13} + 24 q^{15} - 160 q^{16} + 6 q^{17} + 22 q^{19} + 24 q^{23} + 8 q^{24} + 400 q^{25} - 126 q^{27} - 4 q^{28} - 20 q^{30} + 24 q^{31} + 30 q^{33} + 108 q^{35} + 4 q^{36} + 24 q^{38} + 6 q^{39} - 8 q^{42} + 76 q^{43} + 12 q^{44} + 296 q^{45} + 168 q^{47} + 24 q^{48} - 306 q^{49} + 144 q^{50} + 234 q^{51} + 60 q^{52} + 72 q^{53} - 28 q^{54} - 90 q^{57} + 36 q^{60} - 28 q^{61} - 36 q^{62} + 68 q^{63} - 640 q^{64} + 288 q^{65} - 8 q^{66} - 336 q^{67} - 12 q^{68} - 48 q^{69} + 162 q^{71} - 48 q^{72} - 92 q^{73} - 24 q^{74} - 732 q^{75} + 4 q^{76} + 228 q^{77} - 372 q^{78} + 102 q^{79} + 130 q^{81} - 48 q^{82} + 78 q^{83} - 984 q^{87} + 72 q^{88} + 216 q^{89} - 456 q^{90} + 96 q^{91} - 48 q^{92} + 24 q^{93} + 720 q^{95} + 32 q^{96} + 90 q^{97} + 216 q^{98} - 40 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
342.3.t.a $80$ $9.319$ None \(0\) \(-6\) \(0\) \(2\)

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

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