Properties

Label 91.8.bc
Level $91$
Weight $8$
Character orbit 91.bc
Rep. character $\chi_{91}(6,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $256$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
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 272 272 0
Cusp forms 256 256 0
Eisenstein series 16 16 0

Trace form

\( 256 q - 8 q^{2} - 12 q^{4} - 2576 q^{7} - 520 q^{8} + 90392 q^{9} + O(q^{10}) \) \( 256 q - 8 q^{2} - 12 q^{4} - 2576 q^{7} - 520 q^{8} + 90392 q^{9} + 140 q^{11} + 18952 q^{14} - 5144 q^{15} + 524284 q^{16} - 49780 q^{18} + 105576 q^{21} - 16068 q^{22} - 12 q^{23} - 82212 q^{28} - 515084 q^{29} - 807756 q^{30} + 664108 q^{32} - 828764 q^{35} - 907920 q^{36} + 336116 q^{37} + 1230908 q^{39} - 2861572 q^{42} + 1445760 q^{43} + 6188328 q^{44} + 7251012 q^{46} - 150672 q^{49} + 6746164 q^{50} - 13243992 q^{53} + 12393168 q^{56} - 6634220 q^{57} - 12046944 q^{58} + 10702124 q^{60} - 13227040 q^{63} + 2971492 q^{65} + 17955336 q^{67} + 14991480 q^{70} + 29025828 q^{71} - 24700280 q^{72} + 2492856 q^{74} - 49919332 q^{78} + 15493808 q^{79} - 47979668 q^{81} - 57449120 q^{84} + 44075300 q^{85} + 52959360 q^{86} + 52919340 q^{88} + 21040608 q^{91} - 132973464 q^{92} + 113964348 q^{93} - 30386388 q^{95} - 71663372 q^{98} + 7655092 q^{99} + O(q^{100}) \)

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.bc.a 91.bc 91.ac $256$ $28.427$ None \(-8\) \(0\) \(0\) \(-2576\) $\mathrm{SU}(2)[C_{12}]$