Properties

Label 43.2.c
Level 43
Weight 2
Character orbit 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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.2.c.a \(2\) \(0.343\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(1\) \(-3\) \(q+q^{2}+(-1+\zeta_{6})q^{3}-q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
43.2.c.b \(4\) \(0.343\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-6\) \(3\) \(2\) \(4\) \(q+(-2-\beta _{2})q^{2}+(1+\beta _{1}+\beta _{3})q^{3}+\cdots\)