Properties

Label 144.2.x
Level $144$
Weight $2$
Character orbit 144.x
Rep. character $\chi_{144}(13,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $88$
Newform subspaces $5$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(144, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 10q^{6} - 8q^{8} + O(q^{10}) \) \( 88q - 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 10q^{6} - 8q^{8} - 8q^{10} - 2q^{11} + 8q^{12} - 2q^{13} - 10q^{14} - 8q^{15} - 2q^{16} - 16q^{17} - 18q^{18} - 8q^{19} + 12q^{20} - 10q^{21} - 2q^{22} - 40q^{24} - 40q^{26} + 8q^{27} - 24q^{28} - 2q^{29} + 6q^{30} - 4q^{31} - 22q^{32} - 8q^{33} - 6q^{34} - 28q^{35} + 14q^{36} - 8q^{37} + 26q^{38} - 2q^{40} - 16q^{42} - 2q^{43} + 36q^{44} - 14q^{45} + 8q^{46} - 44q^{47} + 2q^{48} + 16q^{49} - 36q^{50} - 36q^{51} - 2q^{52} - 8q^{53} + 74q^{54} + 52q^{56} - 20q^{58} + 10q^{59} + 30q^{60} - 2q^{61} + 100q^{62} - 36q^{63} - 44q^{64} - 4q^{65} + 8q^{66} - 2q^{67} + 16q^{68} - 10q^{69} + 12q^{70} + 114q^{72} + 26q^{74} + 56q^{75} + 10q^{76} - 30q^{77} + 88q^{78} - 4q^{79} + 144q^{80} - 8q^{81} - 52q^{82} - 22q^{83} - 22q^{84} - 12q^{85} + 70q^{86} - 26q^{88} + 72q^{90} - 36q^{91} - 56q^{92} - 22q^{93} + 6q^{94} + 60q^{95} + 118q^{96} - 4q^{97} + 40q^{98} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(144, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
144.2.x.a \(4\) \(1.150\) \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-4\) \(12\) \(q+(-1-\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.b \(4\) \(1.150\) \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(-8\) \(-6\) \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.c \(4\) \(1.150\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(6\) \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.d \(4\) \(1.150\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(-12\) \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.e \(72\) \(1.150\) None \(4\) \(2\) \(4\) \(0\)