Properties

Label 91.10.f
Level $91$
Weight $10$
Character orbit 91.f
Rep. character $\chi_{91}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $128$
Newform subspaces $2$
Sturm bound $93$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(93\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 172 128 44
Cusp forms 164 128 36
Eisenstein series 8 0 8

Trace form

\( 128 q - 32 q^{2} - 16896 q^{4} + 4552 q^{5} - 2190 q^{6} + 30996 q^{8} - 445300 q^{9} + O(q^{10}) \) \( 128 q - 32 q^{2} - 16896 q^{4} + 4552 q^{5} - 2190 q^{6} + 30996 q^{8} - 445300 q^{9} - 54872 q^{10} + 36964 q^{11} - 434316 q^{12} + 154744 q^{13} + 307328 q^{14} + 228276 q^{15} - 5244808 q^{16} + 112240 q^{17} - 1051736 q^{18} - 899568 q^{19} - 3281380 q^{20} - 38416 q^{21} - 4112922 q^{22} - 2257252 q^{23} + 2110864 q^{24} + 45303552 q^{25} + 11333010 q^{26} + 8505792 q^{27} - 19043428 q^{29} - 3025192 q^{30} + 11417016 q^{31} + 10158612 q^{32} - 21861828 q^{33} - 2927532 q^{34} - 15107092 q^{35} - 117733362 q^{36} + 13763656 q^{37} + 23232452 q^{38} + 130318628 q^{39} - 52909988 q^{40} + 20678404 q^{41} - 12446784 q^{42} - 1315960 q^{43} - 173815320 q^{44} - 80393364 q^{45} - 93583008 q^{46} + 21239680 q^{47} + 195209534 q^{48} - 368947264 q^{49} + 35055434 q^{50} + 254198656 q^{51} - 125158366 q^{52} - 92685248 q^{53} - 320523420 q^{54} + 39050628 q^{55} - 118013952 q^{56} - 161857712 q^{57} + 328104488 q^{58} + 61922516 q^{59} + 98554660 q^{60} + 257455836 q^{61} + 340357616 q^{62} - 127915676 q^{63} + 4045247964 q^{64} - 391086236 q^{65} - 2400694204 q^{66} + 152710740 q^{67} + 730004808 q^{68} + 335077852 q^{69} - 934546032 q^{70} + 149701700 q^{71} - 1164692144 q^{72} + 1198444584 q^{73} + 372709906 q^{74} + 152310144 q^{75} - 325379050 q^{76} + 823754288 q^{77} - 1867205738 q^{78} + 710722040 q^{79} - 207781648 q^{80} - 3342573724 q^{81} + 1144629934 q^{82} - 2995352736 q^{83} - 679334138 q^{84} - 562762204 q^{85} + 2566456152 q^{86} - 408120592 q^{87} - 7227321894 q^{88} + 1917787936 q^{89} + 13309222104 q^{90} + 772824276 q^{91} + 6785560008 q^{92} - 4501913268 q^{93} - 2601384956 q^{94} - 4884082164 q^{95} + 8223906716 q^{96} + 4205305228 q^{97} - 184473632 q^{98} - 6319532832 q^{99} + O(q^{100}) \)

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.f.a $64$ $46.868$ None \(-48\) \(4\) \(8568\) \(-76832\)
91.10.f.b $64$ $46.868$ None \(16\) \(-4\) \(-4016\) \(76832\)

Decomposition of \(S_{10}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(91, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)