Properties

Label 847.2.be
Level $847$
Weight $2$
Character orbit 847.be
Rep. character $\chi_{847}(17,\cdot)$
Character field $\Q(\zeta_{330})$
Dimension $6880$
Newform subspaces $1$
Sturm bound $176$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.be (of order \(330\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{330})\)
Newform subspaces: \( 1 \)
Sturm bound: \(176\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).

Total New Old
Modular forms 7200 7200 0
Cusp forms 6880 6880 0
Eisenstein series 320 320 0

Trace form

\( 6880 q - 39 q^{2} - 90 q^{3} + 45 q^{4} - 117 q^{5} - 83 q^{7} - 176 q^{8} - 844 q^{9} + O(q^{10}) \) \( 6880 q - 39 q^{2} - 90 q^{3} + 45 q^{4} - 117 q^{5} - 83 q^{7} - 176 q^{8} - 844 q^{9} - 198 q^{10} - 32 q^{11} - 120 q^{12} - 110 q^{14} - 154 q^{15} - 101 q^{16} - 147 q^{17} - 141 q^{18} - 117 q^{19} - 55 q^{21} - 188 q^{22} - 32 q^{23} - 108 q^{24} + 35 q^{25} - 159 q^{26} - 48 q^{28} - 136 q^{29} - 3 q^{30} - 141 q^{31} - 44 q^{32} - 174 q^{33} - 93 q^{35} - 20 q^{36} - 72 q^{37} - 135 q^{38} - 32 q^{39} - 240 q^{40} - 137 q^{42} - 176 q^{43} - 85 q^{44} + 51 q^{45} - 24 q^{46} - 129 q^{47} - 53 q^{49} - 206 q^{50} + 55 q^{51} + 81 q^{52} - 21 q^{53} - 858 q^{54} - 56 q^{56} - 170 q^{57} - 19 q^{58} - 153 q^{59} - 74 q^{60} - 102 q^{61} - 37 q^{63} - 560 q^{64} - 44 q^{65} + 60 q^{66} - 20 q^{67} - 57 q^{68} - 61 q^{70} - 180 q^{71} + 170 q^{72} - 72 q^{73} - 89 q^{74} - 51 q^{75} + 176 q^{77} - 90 q^{78} + 70 q^{79} - 81 q^{80} + 628 q^{81} - 27 q^{82} + 70 q^{84} - 406 q^{85} + 30 q^{86} - 33 q^{87} - 41 q^{88} + 135 q^{89} - 59 q^{91} + 258 q^{92} + 131 q^{93} - 270 q^{94} + 14 q^{95} + 189 q^{96} - 186 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
847.2.be.a 847.be 847.ae $6880$ $6.763$ None \(-39\) \(-90\) \(-117\) \(-83\) $\mathrm{SU}(2)[C_{330}]$