Properties

Label 91.8.u
Level $91$
Weight $8$
Character orbit 91.u
Rep. character $\chi_{91}(30,\cdot)$
Character field $\Q(\zeta_{6})$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + O(q^{10}) \) \( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98} + O(q^{100}) \)

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.u.a 91.u 91.u $126$ $28.427$ None \(-3\) \(-164\) \(0\) \(754\) $\mathrm{SU}(2)[C_{6}]$