Properties

Label 43.2.g
Level $43$
Weight $2$
Character orbit 43.g
Rep. character $\chi_{43}(9,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $36$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 43.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 60 60 0
Cusp forms 36 36 0
Eisenstein series 24 24 0

Trace form

\( 36q - 10q^{2} - 16q^{3} - 18q^{4} - 17q^{5} - 4q^{6} + 6q^{7} + 18q^{8} - q^{9} + O(q^{10}) \) \( 36q - 10q^{2} - 16q^{3} - 18q^{4} - 17q^{5} - 4q^{6} + 6q^{7} + 18q^{8} - q^{9} - 7q^{10} - 4q^{11} + 2q^{12} + 18q^{14} - 3q^{15} - 10q^{16} - 10q^{17} + 11q^{18} + 10q^{19} - 3q^{20} - 21q^{21} - 3q^{22} + 4q^{23} + 31q^{24} - 2q^{25} - 15q^{26} - 4q^{27} + 20q^{28} + 9q^{29} + 88q^{30} + 40q^{31} + 48q^{32} - 11q^{33} - 42q^{34} + 11q^{35} - 47q^{36} - 19q^{37} - 21q^{38} - q^{39} - 97q^{40} - 28q^{41} + 2q^{42} - 8q^{43} + 14q^{44} - 46q^{45} - 61q^{46} - 30q^{47} - 97q^{48} + 6q^{49} - 3q^{50} + 57q^{51} - 8q^{52} - 24q^{53} + 6q^{54} + 14q^{55} + 39q^{56} + 52q^{57} + 64q^{58} - q^{59} + 111q^{60} - 14q^{61} + 33q^{62} + 47q^{63} + 48q^{64} + 38q^{65} + 79q^{66} + 66q^{67} + 66q^{68} - 7q^{69} + 47q^{70} - 33q^{71} + 26q^{72} + 29q^{73} - 40q^{74} - 55q^{75} - 39q^{76} - 27q^{77} - 126q^{78} - 17q^{79} + 8q^{80} + 38q^{81} - 54q^{82} - 23q^{83} - 155q^{84} - 56q^{85} - 45q^{86} - 86q^{87} - 17q^{88} - 19q^{89} - 127q^{90} - 13q^{91} - 18q^{92} - 30q^{93} + 44q^{94} + q^{95} - 36q^{96} - 31q^{97} - 5q^{98} - 31q^{99} + O(q^{100}) \)

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.g.a \(36\) \(0.343\) None \(-10\) \(-16\) \(-17\) \(6\)