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Properties

Label 91.8.f
Level $91$
Weight $8$
Character orbit 91.f
Rep. character $\chi_{91}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $2$
Sturm bound $74$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(74\)
Trace bound: \(2\)

Dimensions

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

Total New Old
Modular forms 136 96 40
Cusp forms 128 96 32
Eisenstein series 8 0 8

Trace form

\( 96 q + 16 q^{2} - 2944 q^{4} - 776 q^{5} - 174 q^{6} - 11340 q^{8} - 32650 q^{9} + O(q^{10}) \) \( 96 q + 16 q^{2} - 2944 q^{4} - 776 q^{5} - 174 q^{6} - 11340 q^{8} - 32650 q^{9} + 9368 q^{10} - 7226 q^{11} + 54708 q^{12} - 12346 q^{13} - 21952 q^{14} + 4854 q^{15} - 171464 q^{16} + 27010 q^{17} - 383672 q^{18} - 28328 q^{19} + 170684 q^{20} + 56252 q^{21} + 234166 q^{22} + 127868 q^{23} - 190064 q^{24} + 1723100 q^{25} + 137394 q^{26} - 290772 q^{27} + 435314 q^{29} + 805016 q^{30} + 716300 q^{31} + 541236 q^{32} + 373806 q^{33} + 920116 q^{34} + 313502 q^{35} - 1233330 q^{36} - 28408 q^{37} - 2419036 q^{38} - 1682308 q^{39} - 2738980 q^{40} - 415760 q^{41} + 296352 q^{42} - 604234 q^{43} + 8437416 q^{44} - 1428186 q^{45} + 3202048 q^{46} + 1778476 q^{47} - 8475682 q^{48} - 5647152 q^{49} - 222262 q^{50} - 10834148 q^{51} - 735694 q^{52} - 6333152 q^{53} + 10926468 q^{54} - 1118466 q^{55} + 2107392 q^{56} + 12158380 q^{57} - 5517928 q^{58} + 12400622 q^{59} - 14778428 q^{60} - 2618472 q^{61} + 14521952 q^{62} - 616028 q^{63} + 1572892 q^{64} - 19308086 q^{65} - 18152860 q^{66} + 4076900 q^{67} + 6530808 q^{68} + 8689300 q^{69} + 17995152 q^{70} - 5151784 q^{71} + 50248768 q^{72} - 8497648 q^{73} - 1727966 q^{74} - 795354 q^{75} - 15802426 q^{76} - 11143384 q^{77} - 41219162 q^{78} - 8713784 q^{79} + 49120112 q^{80} - 11251324 q^{81} - 11791234 q^{82} + 40289916 q^{83} + 1073590 q^{84} + 41997346 q^{85} + 47799576 q^{86} - 9804910 q^{87} + 76501530 q^{88} - 8719952 q^{89} - 123421512 q^{90} - 11956294 q^{91} - 35273208 q^{92} + 23576166 q^{93} + 7027044 q^{94} + 48385206 q^{95} + 94070972 q^{96} - 41978722 q^{97} + 1882384 q^{98} - 53482788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.f.a 91.f 13.c $48$ $28.427$ None \(-8\) \(41\) \(526\) \(8232\) $\mathrm{SU}(2)[C_{3}]$
91.8.f.b 91.f 13.c $48$ $28.427$ None \(24\) \(-41\) \(-1302\) \(-8232\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(91, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(91, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)