Properties

Label 547.2.e
Level 547
Weight 2
Character orbit e
Rep. character \(\chi_{547}(9,\cdot)\)
Character field \(\Q(\zeta_{7})\)
Dimension 264
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.e (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{7})\)
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 276 276 0
Cusp forms 264 264 0
Eisenstein series 12 12 0

Trace form

\( 264q - 2q^{2} - q^{3} - 44q^{4} - 3q^{5} - 10q^{6} - 18q^{7} - q^{8} - 35q^{9} + O(q^{10}) \) \( 264q - 2q^{2} - q^{3} - 44q^{4} - 3q^{5} - 10q^{6} - 18q^{7} - q^{8} - 35q^{9} + 13q^{10} - 4q^{11} + 31q^{12} + 7q^{13} - 44q^{14} + 7q^{15} - 76q^{16} + 13q^{17} - 22q^{18} + 11q^{19} + 30q^{20} + 42q^{21} - 28q^{22} + 21q^{23} + 85q^{24} - 37q^{25} - 150q^{26} - 46q^{27} + 34q^{28} + 25q^{29} + 10q^{30} - 25q^{31} + 44q^{32} - 18q^{33} + 41q^{34} - 3q^{35} + 21q^{36} - 29q^{37} - 18q^{38} - 11q^{39} + 90q^{40} - 42q^{41} + 11q^{42} - 43q^{43} - 22q^{44} - 26q^{45} + 78q^{46} - 6q^{47} + 31q^{48} - 70q^{49} + 6q^{50} - 54q^{51} + 87q^{52} + 6q^{53} - 20q^{54} - 5q^{55} - 127q^{56} + 61q^{57} + 10q^{58} - 16q^{59} + 30q^{60} + 27q^{61} + 26q^{62} - 29q^{63} - 57q^{64} - 52q^{65} + 39q^{66} - 2q^{67} - 8q^{68} - 55q^{69} - 34q^{70} - 3q^{71} - 82q^{72} - 8q^{73} + 7q^{74} - 136q^{75} + 125q^{76} - 11q^{77} + 10q^{78} - 15q^{79} - q^{80} - 79q^{81} - 75q^{82} - 72q^{83} - 96q^{84} - 3q^{85} + 121q^{86} + 33q^{87} - 20q^{88} - 60q^{89} - 31q^{90} + 51q^{91} + 104q^{92} + 44q^{93} - 58q^{94} + 95q^{95} - 162q^{96} - 45q^{97} + 103q^{98} - 234q^{99} + O(q^{100}) \)

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.e.a \(264\) \(4.368\) None \(-2\) \(-1\) \(-3\) \(-18\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database