Properties

Label 847.2.u
Level 847
Weight 2
Character orbit u
Rep. character \(\chi_{847}(23,\cdot)\)
Character field \(\Q(\zeta_{33})\)
Dimension 1720
Newform subspaces 1
Sturm bound 176
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 847.u (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 847 \)
Character field: \(\Q(\zeta_{33})\)
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 1800 1800 0
Cusp forms 1720 1720 0
Eisenstein series 80 80 0

Trace form

\( 1720q - 11q^{2} - 20q^{3} + 73q^{4} - 7q^{5} + 8q^{6} - 24q^{7} - 32q^{8} - 844q^{9} + O(q^{10}) \) \( 1720q - 11q^{2} - 20q^{3} + 73q^{4} - 7q^{5} + 8q^{6} - 24q^{7} - 32q^{8} - 844q^{9} - 39q^{10} - 22q^{11} + 49q^{12} - 28q^{13} - 8q^{14} - 26q^{15} + 61q^{16} - 17q^{17} - 2q^{18} - 13q^{19} - 76q^{20} + 13q^{21} - 132q^{22} + 23q^{23} - 36q^{24} + 75q^{25} + 7q^{26} + 28q^{27} - 38q^{28} - 20q^{29} + 51q^{30} - 5q^{31} - 23q^{32} + 59q^{33} + 4q^{34} - 16q^{35} - 18q^{36} - 52q^{37} - 13q^{38} - 46q^{39} + 110q^{40} - 52q^{41} + 33q^{42} - 48q^{43} - 4q^{44} + 60q^{45} - 45q^{46} - 19q^{47} - 2q^{48} - 92q^{49} - 68q^{50} + 127q^{51} - 75q^{52} - 97q^{53} - 213q^{54} - 60q^{55} - 18q^{56} - 18q^{57} + 54q^{58} - 7q^{59} - 20q^{60} - 23q^{61} - 64q^{62} + 125q^{63} - 412q^{64} + 19q^{65} - 46q^{66} + 7q^{67} - 27q^{68} - 6q^{69} - 40q^{70} - 24q^{71} - 11q^{72} - 25q^{73} + 29q^{74} + 81q^{75} + 184q^{76} - 284q^{77} + 2q^{78} - 55q^{79} + 7q^{80} - 772q^{81} + 27q^{82} + 8q^{83} - q^{84} - 232q^{85} - 37q^{86} - 38q^{87} + 23q^{88} - 126q^{89} + 448q^{90} + 17q^{91} + 416q^{92} + 2q^{93} + 144q^{94} + 69q^{95} - 47q^{96} - 62q^{97} + 96q^{98} + 330q^{99} + O(q^{100}) \)

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.u.a \(1720\) \(6.763\) None \(-11\) \(-20\) \(-7\) \(-24\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database