Properties

Label 43.8.c
Level $43$
Weight $8$
Character orbit 43.c
Rep. character $\chi_{43}(6,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $50$
Newform subspaces $1$
Sturm bound $29$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 43.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(29\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(43, [\chi])\).

Total New Old
Modular forms 54 54 0
Cusp forms 50 50 0
Eisenstein series 4 4 0

Trace form

\( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + O(q^{10}) \) \( 50 q + 26 q^{2} - 2 q^{3} + 3014 q^{4} - 249 q^{5} - 1281 q^{6} - 687 q^{7} + 5496 q^{8} - 13389 q^{9} + 1667 q^{10} - 4594 q^{11} - 8448 q^{12} + 2972 q^{13} - 15928 q^{14} - 2485 q^{15} + 185846 q^{16} + 25298 q^{17} + 13249 q^{18} + 3269 q^{19} + 2705 q^{20} - 85260 q^{21} + 150968 q^{22} - 19120 q^{23} - 55070 q^{24} - 296876 q^{25} - 139545 q^{26} - 274154 q^{27} - 118970 q^{28} - 231057 q^{29} + 240447 q^{30} - 177637 q^{31} + 1254274 q^{32} - 344986 q^{33} + 104923 q^{34} - 518850 q^{35} + 816168 q^{36} + 885140 q^{37} + 200956 q^{38} - 59884 q^{39} + 160425 q^{40} + 2202852 q^{41} - 349786 q^{42} + 1009342 q^{43} - 1012518 q^{44} + 775768 q^{45} - 1277532 q^{46} - 2784982 q^{47} - 2238049 q^{48} - 1241240 q^{49} - 5126146 q^{50} - 2477574 q^{51} - 268404 q^{52} - 398258 q^{53} + 6491644 q^{54} - 2551752 q^{55} - 4471819 q^{56} + 2094777 q^{57} - 2294852 q^{58} + 5664766 q^{59} + 1374965 q^{60} + 2652290 q^{61} - 5621243 q^{62} - 3210173 q^{63} + 5395148 q^{64} + 22093214 q^{65} - 284525 q^{66} + 5696184 q^{67} + 2422800 q^{68} + 4199245 q^{69} - 8874170 q^{70} - 16652990 q^{71} + 5916954 q^{72} + 108058 q^{73} + 8260200 q^{74} - 3594466 q^{75} - 7386456 q^{76} - 8874183 q^{77} - 27627308 q^{78} - 7378370 q^{79} + 7523523 q^{80} - 14862361 q^{81} + 7898428 q^{82} + 18099816 q^{83} + 47917640 q^{84} + 5843026 q^{85} + 14578342 q^{86} - 24244628 q^{87} + 23110740 q^{88} - 20405960 q^{89} + 32640076 q^{90} + 10283016 q^{91} - 27186571 q^{92} - 19267997 q^{93} - 52636002 q^{94} + 1708621 q^{95} + 8113092 q^{96} + 53505940 q^{97} - 3752059 q^{98} + 10929650 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
43.8.c.a 43.c 43.c $50$ $13.433$ None \(26\) \(-2\) \(-249\) \(-687\) $\mathrm{SU}(2)[C_{3}]$