Properties

Label 91.10.k
Level $91$
Weight $10$
Character orbit 91.k
Rep. character $\chi_{91}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $164$
Newform subspaces $1$
Sturm bound $93$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(93\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(91, [\chi])\).

Total New Old
Modular forms 172 172 0
Cusp forms 164 164 0
Eisenstein series 8 8 0

Trace form

\( 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9} + O(q^{10}) \) \( 164 q - 161 q^{3} - 40962 q^{4} - 6 q^{6} - 2055 q^{7} - 510909 q^{9} + 41025 q^{10} - 85389 q^{11} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} + 9425286 q^{16} - 1277590 q^{17} + 1176873 q^{18} - 1344159 q^{19} + 571062 q^{20} - 1367523 q^{21} - 1417332 q^{22} - 2148066 q^{23} + 62118 q^{24} + 29660776 q^{25} + 3184908 q^{26} + 7350574 q^{27} + 4828755 q^{28} + 996812 q^{29} - 9177016 q^{30} - 21474090 q^{31} - 15796239 q^{33} + 10592613 q^{35} + 131881331 q^{36} - 8950274 q^{38} - 35258971 q^{39} - 7901342 q^{40} + 24649770 q^{41} - 51088299 q^{42} + 15892214 q^{43} - 1176612 q^{44} - 69222114 q^{47} - 15455476 q^{48} - 57160671 q^{49} + 309166224 q^{50} + 52823362 q^{51} + 177629625 q^{52} - 155327528 q^{53} - 77925569 q^{55} - 92078463 q^{56} - 597924735 q^{58} - 290928939 q^{60} - 468761537 q^{61} + 238770500 q^{62} - 358980429 q^{63} - 2035250696 q^{64} - 542245158 q^{65} - 154929237 q^{66} - 353402973 q^{67} + 1196053594 q^{68} + 127053056 q^{69} - 1180478502 q^{70} - 269829840 q^{71} - 485282307 q^{72} - 35353098 q^{73} + 920062914 q^{74} - 1606576144 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} - 432598794 q^{80} - 1724339502 q^{81} - 324994534 q^{82} + 3803919051 q^{84} - 196261605 q^{85} + 572477022 q^{86} + 3699935866 q^{87} + 37403221 q^{88} - 9086462948 q^{90} + 2603275581 q^{91} - 2683122798 q^{92} - 2561821264 q^{94} - 397964902 q^{95} + 392112 q^{96} + 6155159124 q^{97} + 2492693148 q^{98} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(91, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
91.10.k.a $164$ $46.868$ None \(0\) \(-161\) \(0\) \(-2055\)