Properties

Label 342.3.q
Level $342$
Weight $3$
Character orbit 342.q
Rep. character $\chi_{342}(83,\cdot)$
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.q (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

\( 80q + 4q^{3} - 160q^{4} - 8q^{6} - 2q^{7} + 4q^{9} + O(q^{10}) \) \( 80q + 4q^{3} - 160q^{4} - 8q^{6} - 2q^{7} + 4q^{9} + 18q^{11} - 8q^{12} - 20q^{13} - 2q^{15} + 320q^{16} + 90q^{17} - 16q^{18} - 22q^{19} + 60q^{21} + 12q^{22} + 16q^{24} + 200q^{25} + 70q^{27} + 4q^{28} + 54q^{29} - 44q^{30} - 8q^{31} - 22q^{33} + 48q^{34} - 8q^{36} - 44q^{37} + 36q^{38} + 78q^{39} + 162q^{41} + 80q^{42} + 88q^{43} - 36q^{44} - 88q^{45} - 72q^{47} + 16q^{48} - 306q^{49} + 432q^{50} + 154q^{51} + 40q^{52} - 72q^{53} + 208q^{54} + 36q^{59} + 4q^{60} - 14q^{61} - 108q^{62} + 64q^{63} - 640q^{64} - 144q^{65} - 96q^{66} - 56q^{67} - 180q^{68} - 136q^{69} - 270q^{71} + 32q^{72} - 104q^{73} - 72q^{75} + 44q^{76} + 432q^{77} + 112q^{78} - 68q^{79} - 260q^{81} + 48q^{82} + 342q^{83} - 120q^{84} + 860q^{87} - 24q^{88} - 216q^{89} + 272q^{90} - 340q^{91} - 224q^{93} - 756q^{95} - 32q^{96} - 212q^{97} - 216q^{98} + 100q^{99} + O(q^{100}) \)

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.q.a \(80\) \(9.319\) None \(0\) \(4\) \(0\) \(-2\)

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

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