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

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

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.be.a \(6880\) \(6.763\) None \(-39\) \(-90\) \(-117\) \(-83\)