Properties

Label 847.2.bc
Level $847$
Weight $2$
Character orbit 847.bc
Rep. character $\chi_{847}(4,\cdot)$
Character field $\Q(\zeta_{165})$
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.bc (of order \(165\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{165})\)
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

\( 6880q - 39q^{2} - 30q^{3} - 123q^{4} - 43q^{5} - 208q^{6} - 81q^{7} - 148q^{8} + 784q^{9} + O(q^{10}) \) \( 6880q - 39q^{2} - 30q^{3} - 123q^{4} - 43q^{5} - 208q^{6} - 81q^{7} - 148q^{8} + 784q^{9} - 26q^{10} - 28q^{11} - 94q^{12} - 172q^{13} - 102q^{14} - 174q^{15} - 121q^{16} - 33q^{17} - 73q^{18} - 37q^{19} - 144q^{20} - 103q^{21} - 128q^{22} - 68q^{23} - 4q^{24} - 145q^{25} - 37q^{26} - 258q^{27} - 92q^{28} - 200q^{29} - 131q^{30} - 35q^{31} - 32q^{32} - 84q^{33} - 184q^{34} - 69q^{35} - 212q^{36} - 18q^{37} - 37q^{38} - 44q^{39} - 170q^{40} - 238q^{41} - 63q^{42} - 132q^{43} - 61q^{44} - 105q^{45} - 60q^{46} - 61q^{47} - 348q^{48} + 27q^{49} - 182q^{50} - 197q^{51} + 25q^{52} + 47q^{53} + 88q^{54} - 180q^{55} - 72q^{56} - 262q^{57} - 69q^{58} - 43q^{59} + 20q^{60} - 62q^{61} - 96q^{62} - 275q^{63} + 112q^{64} - 34q^{65} + 36q^{66} - 52q^{67} - 23q^{68} - 124q^{69} - 105q^{70} - 196q^{71} + 26q^{72} - 70q^{73} + 11q^{74} - 91q^{75} - 164q^{76} + 144q^{77} - 182q^{78} - 30q^{79} - 77q^{80} + 772q^{81} - 57q^{82} - 148q^{83} - 94q^{84} + 142q^{85} - 48q^{86} - 77q^{87} - 93q^{88} + 81q^{89} - 598q^{90} - 157q^{91} - 586q^{92} - 97q^{93} - 254q^{94} - 154q^{95} + 77q^{96} - 198q^{97} - 296q^{98} - 510q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
847.2.bc.a \(6880\) \(6.763\) None \(-39\) \(-30\) \(-43\) \(-81\)