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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
144.2.x.a 144.x 144.x $4$ $1.150$ \(\Q(\zeta_{12})\) None \(-4\) \(0\) \(-4\) \(12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1-\zeta_{12}^{3})q^{2}+(2\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.b 144.x 144.x $4$ $1.150$ \(\Q(\zeta_{12})\) None \(-2\) \(-6\) \(-8\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-2+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.c 144.x 144.x $4$ $1.150$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
144.2.x.d 144.x 144.x $4$ $1.150$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(2\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+2\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
144.2.x.e 144.x 144.x $72$ $1.150$ None \(4\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{12}]$