Properties

Label 43.5.h
Level $43$
Weight $5$
Character orbit 43.h
Rep. character $\chi_{43}(3,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $168$
Newform subspaces $1$
Sturm bound $18$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(43, [\chi])\).

Total New Old
Modular forms 192 192 0
Cusp forms 168 168 0
Eisenstein series 24 24 0

Trace form

\( 168 q - 14 q^{2} - 20 q^{3} + 220 q^{4} - 11 q^{5} - 22 q^{6} - 150 q^{7} + 322 q^{8} - 660 q^{9} + O(q^{10}) \) \( 168 q - 14 q^{2} - 20 q^{3} + 220 q^{4} - 11 q^{5} - 22 q^{6} - 150 q^{7} + 322 q^{8} - 660 q^{9} - 105 q^{10} + 362 q^{11} + 1124 q^{12} - 166 q^{13} - 876 q^{14} + 1157 q^{15} - 2752 q^{16} - 37 q^{17} + 988 q^{18} - 1004 q^{19} + 1909 q^{20} - 2265 q^{21} + 2338 q^{22} - 976 q^{23} + 3016 q^{24} - 2199 q^{25} + 1957 q^{26} - 14 q^{27} + 2022 q^{28} + 571 q^{29} - 7896 q^{30} - 7476 q^{31} + 21616 q^{32} - 2900 q^{33} - 1559 q^{34} - 1623 q^{35} - 9123 q^{36} - 11949 q^{37} - 19394 q^{38} + 175 q^{39} - 10317 q^{40} - 4162 q^{41} + 1005 q^{43} + 744 q^{44} + 16632 q^{45} + 34415 q^{46} + 8486 q^{47} + 37831 q^{48} + 20918 q^{49} + 14433 q^{50} + 25270 q^{51} - 40864 q^{52} - 7522 q^{53} + 23330 q^{54} - 30896 q^{55} - 38943 q^{56} + 14884 q^{57} - 2644 q^{58} - 2743 q^{59} - 15231 q^{60} - 164 q^{61} + 15097 q^{62} - 22771 q^{63} - 7274 q^{64} + 19138 q^{65} + 16631 q^{66} - 31599 q^{67} - 17923 q^{68} + 49515 q^{69} + 69209 q^{70} - 2057 q^{71} + 62621 q^{72} - 19678 q^{73} - 86988 q^{74} - 28525 q^{75} - 38694 q^{76} - 65721 q^{77} - 112636 q^{78} - 293 q^{79} - 99738 q^{80} - 38860 q^{81} - 40460 q^{82} - 45580 q^{83} - 28041 q^{84} + 6292 q^{86} + 2598 q^{87} + 48902 q^{88} + 83608 q^{89} + 180383 q^{90} + 62161 q^{91} + 39390 q^{92} + 203670 q^{93} + 199878 q^{94} - 20897 q^{95} + 59662 q^{96} + 93627 q^{97} - 40724 q^{98} + 26734 q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
43.5.h.a 43.h 43.h $168$ $4.445$ None \(-14\) \(-20\) \(-11\) \(-150\) $\mathrm{SU}(2)[C_{42}]$