Properties

Label 547.2.f
Level 547
Weight 2
Character orbit f
Rep. character \(\chi_{547}(46,\cdot)\)
Character field \(\Q(\zeta_{13})\)
Dimension 528
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.f (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{13})\)
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 552 552 0
Cusp forms 528 528 0
Eisenstein series 24 24 0

Trace form

\( 528q - 8q^{2} - 46q^{3} - 50q^{4} - 9q^{5} - 21q^{6} - 3q^{7} + 14q^{8} + 466q^{9} + O(q^{10}) \) \( 528q - 8q^{2} - 46q^{3} - 50q^{4} - 9q^{5} - 21q^{6} - 3q^{7} + 14q^{8} + 466q^{9} + 7q^{10} - 16q^{11} - 53q^{12} - 12q^{13} - 38q^{15} - 38q^{16} + 7q^{17} - 23q^{18} + 5q^{19} + 45q^{20} + 4q^{21} + 43q^{22} + 2q^{23} - 51q^{24} - 69q^{25} - 4q^{26} - 142q^{27} - 2q^{28} - 72q^{29} - 50q^{30} + 25q^{31} + 66q^{32} - 4q^{34} + 33q^{35} - 55q^{36} + 21q^{37} + 40q^{38} - 142q^{39} + 78q^{40} - 140q^{41} - 248q^{42} + 23q^{43} + 64q^{44} - 163q^{45} + 14q^{46} + 37q^{47} - 35q^{48} + q^{49} + 70q^{50} - 72q^{51} - 74q^{52} - 17q^{53} - 76q^{54} + 6q^{55} - 38q^{56} + 5q^{57} + 29q^{58} + 30q^{59} - 108q^{60} - 94q^{61} - 75q^{62} - 77q^{63} - 252q^{64} - 122q^{65} + 79q^{66} + 43q^{67} - 193q^{68} + 14q^{69} - 267q^{70} + 61q^{71} + 49q^{72} + 11q^{73} + 85q^{74} + 120q^{75} - 23q^{76} + 31q^{77} - 90q^{78} + 65q^{79} + 58q^{80} + 280q^{81} + 10q^{82} - 8q^{83} - 136q^{84} + 33q^{85} + 91q^{86} - 70q^{87} - 198q^{88} + 41q^{89} - 68q^{90} + 38q^{91} + 43q^{92} + 132q^{93} + 8q^{94} - 49q^{95} + 262q^{96} - 14q^{97} + 41q^{98} - 36q^{99} + O(q^{100}) \)

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.f.a \(528\) \(4.368\) None \(-8\) \(-46\) \(-9\) \(-3\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database