Properties

Label 91.10.u
Level $91$
Weight $10$
Character orbit 91.u
Rep. character $\chi_{91}(30,\cdot)$
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.u (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

\( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9} + O(q^{10}) \) \( 164 q - 3 q^{2} + 322 q^{3} + 20481 q^{4} - 6 q^{6} + 1023 q^{7} + 1021818 q^{9} - 82050 q^{10} + 43064 q^{12} - 232462 q^{13} + 82708 q^{14} + 338445 q^{15} - 4712643 q^{16} + 638795 q^{17} - 1176873 q^{18} + 571062 q^{20} + 1367523 q^{21} - 1417332 q^{22} + 1074033 q^{23} + 29660776 q^{25} - 4350684 q^{26} + 7350574 q^{27} - 5807904 q^{28} + 996812 q^{29} + 18354032 q^{30} + 21474090 q^{31} + 786429 q^{32} - 14921172 q^{35} + 131881331 q^{36} + 6476901 q^{37} - 8950274 q^{38} + 27439160 q^{39} - 7901342 q^{40} + 24649770 q^{41} + 107058858 q^{42} + 15892214 q^{43} + 1176612 q^{44} + 20834727 q^{45} + 277543272 q^{46} + 69222114 q^{47} - 15455476 q^{48} - 69917499 q^{49} + 309166224 q^{50} + 52823362 q^{51} - 95118408 q^{52} - 155327528 q^{53} + 82174923 q^{54} - 77925569 q^{55} - 282686919 q^{56} - 216056427 q^{59} + 290928939 q^{60} + 937523074 q^{61} + 238770500 q^{62} - 521903604 q^{63} - 2035250696 q^{64} + 418729590 q^{65} - 154929237 q^{66} - 598026797 q^{68} + 127053056 q^{69} + 1180478502 q^{70} - 269829840 q^{71} + 35353098 q^{73} - 460031457 q^{74} + 803288072 q^{75} + 1140965370 q^{76} - 1032378781 q^{77} - 835494667 q^{78} - 683323974 q^{79} + 3448679004 q^{81} + 649989068 q^{82} + 2491042464 q^{84} - 196261605 q^{85} - 572477022 q^{86} - 1849967933 q^{87} - 74806442 q^{88} - 207815607 q^{89} - 9086462948 q^{90} - 1222123653 q^{91} - 2683122798 q^{92} + 389990277 q^{93} + 5123642528 q^{94} + 198982451 q^{95} - 392112 q^{96} + 6155159124 q^{97} + 1935772011 q^{98} + O(q^{100}) \)

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.u.a $164$ $46.868$ None \(-3\) \(322\) \(0\) \(1023\)