Properties

Label 144.3.v
Level $144$
Weight $3$
Character orbit 144.v
Rep. character $\chi_{144}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $184$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(144, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184q - 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 8q^{8} + O(q^{10}) \) \( 184q - 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} + 2q^{6} - 4q^{7} - 8q^{8} - 8q^{10} - 2q^{11} + 56q^{12} - 2q^{13} + 14q^{14} - 2q^{16} - 16q^{17} + 38q^{18} - 8q^{19} - 44q^{20} + 14q^{21} - 2q^{22} - 4q^{23} + 120q^{24} - 104q^{26} - 52q^{27} + 56q^{28} - 2q^{29} - 130q^{30} - 182q^{32} - 8q^{33} - 10q^{34} + 92q^{35} - 2q^{36} - 8q^{37} - 254q^{38} + 184q^{39} - 2q^{40} - 252q^{42} - 2q^{43} - 140q^{44} - 54q^{45} + 176q^{46} + 162q^{48} - 480q^{49} - 96q^{50} - 120q^{51} - 2q^{52} - 8q^{53} + 94q^{54} - 16q^{55} + 260q^{56} + 88q^{58} + 142q^{59} - 434q^{60} - 2q^{61} - 636q^{62} + 244q^{64} - 4q^{65} - 100q^{66} - 2q^{67} - 112q^{68} + 14q^{69} - 100q^{70} - 16q^{71} + 98q^{72} + 82q^{74} - 296q^{75} + 154q^{76} + 194q^{77} + 228q^{78} + 592q^{80} - 8q^{81} - 420q^{82} + 238q^{83} - 22q^{84} - 52q^{85} - 170q^{86} - 456q^{87} - 26q^{88} + 808q^{90} + 188q^{91} + 176q^{92} + 26q^{93} - 18q^{94} - 202q^{96} - 4q^{97} + 408q^{98} - 38q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.3.v.a \(184\) \(3.924\) None \(-2\) \(-4\) \(-2\) \(-4\)