Properties

Label 547.2.j
Level 547
Weight 2
Character orbit j
Rep. character \(\chi_{547}(11,\cdot)\)
Character field \(\Q(\zeta_{39})\)
Dimension 1080
Newform subspaces 1
Sturm bound 91
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.j (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{39})\)
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 1128 1128 0
Cusp forms 1080 1080 0
Eisenstein series 48 48 0

Trace form

\( 1080q - 25q^{2} - 74q^{3} + 21q^{4} - 27q^{5} - 75q^{6} - 28q^{7} + 4q^{8} + 1010q^{9} + O(q^{10}) \) \( 1080q - 25q^{2} - 74q^{3} + 21q^{4} - 27q^{5} - 75q^{6} - 28q^{7} + 4q^{8} + 1010q^{9} - 16q^{10} - 14q^{11} - 69q^{12} - 10q^{13} - 15q^{14} - 97q^{15} + 39q^{16} - 22q^{17} - 145q^{18} - 24q^{19} - 51q^{20} - 77q^{21} - 19q^{22} - 53q^{23} - 45q^{24} + 40q^{25} - 68q^{26} - 278q^{27} - 50q^{28} + 39q^{29} + 14q^{30} - 2q^{31} - 45q^{32} - 105q^{33} - 98q^{34} - 18q^{35} - 172q^{36} - 16q^{37} - 37q^{38} + 30q^{39} - 33q^{40} + 62q^{41} + 170q^{42} + 12q^{43} - 22q^{44} - 128q^{45} + 79q^{46} - 58q^{47} - 27q^{48} + 17q^{49} - 40q^{50} - 39q^{51} + 97q^{52} + 17q^{53} - 278q^{54} + 9q^{55} + 47q^{56} - 174q^{57} - 134q^{58} - 126q^{59} - 414q^{60} - 79q^{61} + 15q^{62} - 398q^{63} - 308q^{64} + 47q^{65} - 142q^{66} + 22q^{67} + 7q^{68} - 77q^{69} + 396q^{70} - 22q^{71} - 172q^{72} + 9q^{73} - 43q^{74} - 143q^{75} + 46q^{76} + 56q^{77} - 33q^{78} + 72q^{79} + 131q^{80} + 944q^{81} + 74q^{82} + 41q^{83} - 582q^{84} - 66q^{85} + 20q^{86} - 182q^{87} - 459q^{88} - 92q^{89} - 265q^{90} + 65q^{91} + 86q^{92} - 28q^{93} - 17q^{94} + 37q^{95} - 70q^{96} + 91q^{97} + 139q^{98} - 237q^{99} + O(q^{100}) \)

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.j.a \(1080\) \(4.368\) None \(-25\) \(-74\) \(-27\) \(-28\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database