Properties

Label 143.2.e
Level $143$
Weight $2$
Character orbit 143.e
Rep. character $\chi_{143}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
Sturm bound $28$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 143.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(143, [\chi])\).

Total New Old
Modular forms 32 24 8
Cusp forms 24 24 0
Eisenstein series 8 0 8

Trace form

\( 24 q - 2 q^{2} - 2 q^{3} - 12 q^{4} - 8 q^{5} + 6 q^{6} - 2 q^{7} - 14 q^{9} + O(q^{10}) \) \( 24 q - 2 q^{2} - 2 q^{3} - 12 q^{4} - 8 q^{5} + 6 q^{6} - 2 q^{7} - 14 q^{9} + 6 q^{10} - 4 q^{12} - 10 q^{13} + 8 q^{14} - 16 q^{15} - 8 q^{16} + 8 q^{17} + 28 q^{18} + 2 q^{19} + 14 q^{20} - 20 q^{21} - 2 q^{22} - 6 q^{23} + 12 q^{24} + 8 q^{25} + 2 q^{26} + 16 q^{27} - 2 q^{28} + 4 q^{29} - 4 q^{30} + 4 q^{31} - 22 q^{32} - 4 q^{34} - 16 q^{35} - 20 q^{36} + 10 q^{37} + 20 q^{38} + 16 q^{39} - 76 q^{40} + 20 q^{41} + 2 q^{42} + 18 q^{43} - 8 q^{44} + 14 q^{45} + 38 q^{46} - 48 q^{47} + 8 q^{48} - 2 q^{49} - 26 q^{50} - 28 q^{51} + 22 q^{52} + 8 q^{53} + 32 q^{54} - 8 q^{55} - 6 q^{56} + 16 q^{57} - 24 q^{58} - 16 q^{59} + 100 q^{60} + 30 q^{61} + 12 q^{62} - 6 q^{63} - 28 q^{64} - 24 q^{65} + 36 q^{66} - 6 q^{67} + 12 q^{68} + 18 q^{69} - 84 q^{70} - 10 q^{71} - 68 q^{72} - 20 q^{73} + 58 q^{74} + 6 q^{75} - 16 q^{76} + 16 q^{77} + 60 q^{78} - 8 q^{79} + 48 q^{80} - 4 q^{81} - 14 q^{82} - 44 q^{83} + 16 q^{84} - 36 q^{85} - 76 q^{86} + 8 q^{87} + 6 q^{88} - 10 q^{89} - 64 q^{90} + 46 q^{91} + 44 q^{92} - 70 q^{93} + 6 q^{94} + 4 q^{95} + 80 q^{96} - 14 q^{97} + 56 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(143, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
143.2.e.a 143.e 13.c $6$ $1.142$ 6.0.1714608.1 None \(-3\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(-\beta _{3}+\beta _{5})q^{3}-\beta _{4}q^{4}+\cdots\)
143.2.e.b 143.e 13.c $6$ $1.142$ 6.0.3518667.1 None \(1\) \(-1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-3+\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
143.2.e.c 143.e 13.c $12$ $1.142$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-1\) \(-12\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{2}+(\beta _{6}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)