Properties

Label 91.8.g
Level $91$
Weight $8$
Character orbit 91.g
Rep. character $\chi_{91}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $126$
Newform subspaces $1$
Sturm bound $74$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(74\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(91, [\chi])\).

Total New Old
Modular forms 134 134 0
Cusp forms 126 126 0
Eisenstein series 8 8 0

Trace form

\( 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9} + O(q^{10}) \) \( 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9} + 8510 q^{10} - 14846 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} - 205147 q^{16} - 49637 q^{17} - 21111 q^{18} + 9688 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} - 17065 q^{23} + 260608 q^{24} - 810669 q^{25} - 7812 q^{26} + 416614 q^{27} + 425466 q^{28} + 191096 q^{29} - 141332 q^{30} + 183609 q^{31} - 347673 q^{32} - 357182 q^{33} - 742000 q^{34} + 145247 q^{35} - 1732409 q^{36} + 681449 q^{37} - 877438 q^{38} - 1822261 q^{39} - 1502882 q^{40} + 593701 q^{41} - 1525674 q^{42} - 592188 q^{43} + 1254066 q^{44} - 977113 q^{45} + 692726 q^{46} + 98278 q^{47} - 374916 q^{48} - 747844 q^{49} + 289562 q^{50} - 281250 q^{51} - 1459588 q^{52} - 1256681 q^{53} + 146907 q^{54} - 3015554 q^{55} - 5896005 q^{56} + 2743072 q^{57} - 3702938 q^{58} + 1139729 q^{59} + 1031485 q^{60} + 2255272 q^{61} - 7724680 q^{62} - 8617558 q^{63} + 11827496 q^{64} + 487948 q^{65} + 435059 q^{66} - 8746696 q^{67} - 4368561 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} + 23321902 q^{72} - 5060877 q^{73} - 592001 q^{74} - 11318627 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} + 247136 q^{80} + 61513790 q^{81} - 17253904 q^{82} - 18679806 q^{83} + 14270544 q^{84} + 5330093 q^{85} - 8512356 q^{86} + 8254381 q^{87} + 12876438 q^{88} + 3088342 q^{89} + 53481084 q^{90} - 38127665 q^{91} + 2460546 q^{92} - 13841202 q^{93} + 34843588 q^{94} - 19776699 q^{95} + 26667066 q^{96} + 7705262 q^{97} - 58123667 q^{98} - 60531432 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.8.g.a 91.g 91.g $126$ $28.427$ None \(1\) \(160\) \(-2\) \(-1816\) $\mathrm{SU}(2)[C_{3}]$