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Properties

Label 95.11.q
Level $95$
Weight $11$
Character orbit 95.q
Rep. character $\chi_{95}(17,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1176$
Newform subspaces $1$
Sturm bound $110$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.q (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(110\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(95, [\chi])\).

Total New Old
Modular forms 1224 1224 0
Cusp forms 1176 1176 0
Eisenstein series 48 48 0

Trace form

\( 1176 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 14604 q^{6} - 11688 q^{7} - 6 q^{8} + O(q^{10}) \) \( 1176 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 14604 q^{6} - 11688 q^{7} - 6 q^{8} - 12 q^{10} - 12 q^{11} - 6 q^{12} - 12 q^{13} + 3424146 q^{15} - 13618884 q^{16} - 3657378 q^{17} - 23774232 q^{18} + 38894436 q^{20} - 8689704 q^{21} - 22604556 q^{22} - 32885808 q^{23} + 42291732 q^{25} - 319452 q^{26} - 6 q^{27} + 144277488 q^{28} - 6 q^{30} - 12 q^{31} - 304326750 q^{32} + 265207902 q^{33} - 173435754 q^{35} - 288159144 q^{36} - 24 q^{37} + 1298228634 q^{38} - 1334600346 q^{40} + 659462736 q^{41} + 362797044 q^{42} - 961639656 q^{43} + 161157936 q^{45} - 12 q^{46} - 886017372 q^{47} + 1630739472 q^{48} + 2215521786 q^{50} + 1125126576 q^{51} + 6132 q^{52} - 657601770 q^{53} - 3332318022 q^{55} - 48 q^{56} - 967967226 q^{57} - 7596060648 q^{58} + 3688833012 q^{60} + 1851266016 q^{61} + 845228664 q^{62} + 3514567662 q^{63} - 1840657236 q^{65} + 19323290088 q^{66} + 20641904172 q^{67} - 5240868870 q^{68} - 8235161100 q^{70} - 24 q^{71} - 64729344936 q^{72} - 3449985870 q^{73} - 34306313016 q^{75} + 10512445536 q^{76} + 46076293368 q^{77} - 51672410862 q^{78} + 20602412592 q^{80} + 46901590776 q^{81} - 12506757996 q^{82} + 22786639188 q^{83} - 22949887236 q^{85} - 81567902124 q^{86} + 3763013226 q^{87} + 8846542842 q^{88} + 87014491266 q^{90} + 37012815456 q^{91} - 35376892980 q^{92} + 96817414890 q^{93} - 20594188944 q^{95} + 84921616752 q^{96} - 9492824088 q^{97} - 86078409906 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(95, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
95.11.q.a 95.q 95.q $1176$ $60.359$ None \(-12\) \(-12\) \(-12\) \(-11688\) $\mathrm{SU}(2)[C_{36}]$