Properties

Label 547.2.c
Level 547
Weight 2
Character orbit c
Rep. character \(\chi_{547}(40,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 90
Newform subspaces 1
Sturm bound 91
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(91\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(547, [\chi])\).

Total New Old
Modular forms 94 94 0
Cusp forms 90 90 0
Eisenstein series 4 4 0

Trace form

\( 90q - q^{2} - 4q^{3} - 47q^{4} + q^{5} - 3q^{6} + 2q^{7} - 30q^{8} + 82q^{9} + O(q^{10}) \) \( 90q - q^{2} - 4q^{3} - 47q^{4} + q^{5} - 3q^{6} + 2q^{7} - 30q^{8} + 82q^{9} - 10q^{10} + q^{11} + 4q^{12} - 3q^{13} + 2q^{14} - 7q^{15} - 39q^{16} - 4q^{17} - 11q^{18} - 2q^{19} + 25q^{20} - 27q^{21} - 7q^{22} + q^{23} + 32q^{24} - 40q^{25} - 10q^{26} - 34q^{27} - 28q^{28} + 26q^{29} - 40q^{30} - 24q^{31} + 19q^{32} + q^{33} - 6q^{34} - 8q^{35} - 36q^{36} - 10q^{37} + 24q^{38} + 22q^{39} + 20q^{40} + 3q^{41} + 38q^{42} - 12q^{43} - 30q^{44} - 2q^{45} - 40q^{46} + 32q^{47} + 14q^{48} - 43q^{49} + 14q^{50} + 13q^{51} + 46q^{52} + 9q^{53} - 8q^{54} + 4q^{55} - 8q^{56} - 8q^{57} + 4q^{58} + 22q^{59} - 2q^{60} - 12q^{61} + 11q^{62} + 8q^{63} + 22q^{64} + 18q^{65} + 12q^{66} - 22q^{67} + 6q^{68} - q^{69} - 6q^{70} - 4q^{71} - 140q^{72} + 17q^{73} + 17q^{74} + 39q^{75} + 84q^{76} - 4q^{77} + 33q^{78} - 72q^{79} - 40q^{80} + 18q^{81} - 9q^{82} + 24q^{83} + 114q^{84} + 40q^{85} - 72q^{86} - 78q^{87} - 22q^{88} + 14q^{89} + 96q^{90} - 8q^{92} - 76q^{93} + 108q^{94} - 11q^{95} - 34q^{96} - 74q^{98} - 62q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(547, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
547.2.c.a \(90\) \(4.368\) None \(-1\) \(-4\) \(1\) \(2\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database