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Properties

Label 43.2.c
Level $43$
Weight $2$
Character orbit 43.c
Rep. character $\chi_{43}(6,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $6$
Newform subspaces $2$
Sturm bound $7$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(43, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 18 q^{8} + q^{9} + O(q^{10}) \) \( 6 q - 4 q^{2} + 2 q^{3} + 4 q^{4} + 3 q^{5} - 3 q^{6} + q^{7} - 18 q^{8} + q^{9} - 7 q^{10} - 10 q^{11} - 2 q^{12} - 4 q^{14} + 3 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 3 q^{19} + 17 q^{20} + 28 q^{21} + 10 q^{22} - 4 q^{23} + 4 q^{24} + 2 q^{25} + 15 q^{26} - 10 q^{27} - 6 q^{28} - 9 q^{29} + 3 q^{30} - 5 q^{31} - 20 q^{32} - 10 q^{33} - 14 q^{34} - 18 q^{35} + 19 q^{36} + 12 q^{37} + 7 q^{38} - 20 q^{39} - 29 q^{40} - 2 q^{42} - 34 q^{43} + 32 q^{45} + 26 q^{46} + 2 q^{47} + 13 q^{48} - 6 q^{49} + 17 q^{50} - 22 q^{51} - 20 q^{52} + 10 q^{53} - 20 q^{54} + 17 q^{56} - 3 q^{57} + 6 q^{58} + 22 q^{59} - 13 q^{60} + 14 q^{61} - 5 q^{62} + 23 q^{63} + 22 q^{64} - 10 q^{65} + 5 q^{66} + 4 q^{67} + 39 q^{68} + 21 q^{69} + 2 q^{70} - 2 q^{71} - 33 q^{72} - 8 q^{73} + 12 q^{74} + 6 q^{75} - 17 q^{76} - 15 q^{77} + 10 q^{79} + 27 q^{80} - 3 q^{81} - 30 q^{82} - 12 q^{83} - 48 q^{84} + 42 q^{85} + 31 q^{86} - 12 q^{87} + 10 q^{88} - 2 q^{89} - 48 q^{90} + 20 q^{91} - 31 q^{92} - 5 q^{93} - 58 q^{94} + 13 q^{95} - 20 q^{96} - 32 q^{97} - 16 q^{98} + 10 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
43.2.c.a 43.c 43.c $2$ $0.343$ \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
43.2.c.b 43.c 43.c $4$ $0.343$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-6\) \(3\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)