Properties

Label 349.2.g
Level 349
Weight 2
Character orbit g
Rep. character \(\chi_{349}(31,\cdot)\)
Character field \(\Q(\zeta_{29})\)
Dimension 756
Newforms 1
Sturm bound 58
Trace bound 0

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Defining parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.g (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 349 \)
Character field: \(\Q(\zeta_{29})\)
Newforms: \( 1 \)
Sturm bound: \(58\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(349, [\chi])\).

Total New Old
Modular forms 812 812 0
Cusp forms 756 756 0
Eisenstein series 56 56 0

Trace form

\( 756q - 26q^{2} - 25q^{3} - 46q^{4} - 19q^{5} - 9q^{6} - 19q^{7} - 95q^{8} - 44q^{9} + O(q^{10}) \) \( 756q - 26q^{2} - 25q^{3} - 46q^{4} - 19q^{5} - 9q^{6} - 19q^{7} - 95q^{8} - 44q^{9} - 7q^{10} - 25q^{11} - 5q^{12} - 5q^{13} - 9q^{14} - 5q^{15} - 26q^{16} - 11q^{17} - 106q^{18} - 57q^{19} + 15q^{20} - 95q^{21} - 9q^{22} + 11q^{23} + 26q^{24} - 22q^{25} - 35q^{26} + 17q^{27} + 47q^{28} + 9q^{29} + 61q^{30} + 15q^{31} + 16q^{32} + 13q^{33} + 35q^{34} - 27q^{35} + 56q^{36} - 186q^{37} + 37q^{38} + 19q^{39} + 79q^{40} - 33q^{41} - 107q^{42} + 19q^{43} - 93q^{44} + 73q^{45} + 21q^{46} - q^{47} + 39q^{48} + 8q^{49} - 305q^{50} - 83q^{51} - 238q^{52} + q^{53} + 99q^{54} - 81q^{55} + 69q^{56} + 61q^{57} + 97q^{58} + 9q^{59} - 203q^{60} - 227q^{61} + 43q^{62} + 49q^{63} - 151q^{64} + 61q^{65} - 226q^{66} + 53q^{67} + 133q^{68} - 51q^{69} + 165q^{70} + 3q^{71} - 150q^{72} + 71q^{73} - 87q^{74} + 39q^{75} + 159q^{76} + 99q^{77} - 59q^{78} + 33q^{79} - 7q^{80} - 384q^{81} + 107q^{82} - 95q^{83} - 165q^{84} - 36q^{85} + 49q^{86} - 81q^{87} + 101q^{88} - 349q^{89} + 231q^{90} + 107q^{91} + 121q^{92} + 117q^{93} + 157q^{94} - 123q^{95} - 379q^{96} + 57q^{97} - 304q^{98} + 89q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(349, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
349.2.g.a \(756\) \(2.787\) None \(-26\) \(-25\) \(-19\) \(-19\)