Properties

Label 349.2.h
Level 349
Weight 2
Character orbit h
Rep. character \(\chi_{349}(17,\cdot)\)
Character field \(\Q(\zeta_{58})\)
Dimension 784
Newforms 1
Sturm bound 58
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.h (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 349 \)
Character field: \(\Q(\zeta_{58})\)
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 840 840 0
Cusp forms 784 784 0
Eisenstein series 56 56 0

Trace form

\( 784q - 29q^{2} - 25q^{3} + 3q^{4} - 21q^{5} - 29q^{6} - 29q^{7} + 58q^{8} - 57q^{9} + O(q^{10}) \) \( 784q - 29q^{2} - 25q^{3} + 3q^{4} - 21q^{5} - 29q^{6} - 29q^{7} + 58q^{8} - 57q^{9} - 29q^{10} - 29q^{11} - 37q^{12} - 29q^{13} - 33q^{14} - 37q^{15} - 57q^{16} - 21q^{17} - 145q^{18} + 43q^{19} - 35q^{20} - 145q^{21} - 17q^{22} - 13q^{23} - 45q^{25} + 7q^{26} - 43q^{27} - 29q^{28} - 13q^{29} - 29q^{30} - 53q^{31} - 29q^{32} - 29q^{33} - 29q^{34} - 87q^{35} + 33q^{36} + 150q^{37} - 29q^{38} - 29q^{39} - 29q^{40} - 91q^{41} + 145q^{42} - 29q^{43} - 145q^{44} + 23q^{45} - 29q^{46} - 29q^{47} + 111q^{48} + 19q^{49} + 348q^{50} + 61q^{51} - 145q^{52} - 29q^{53} - 29q^{54} - 145q^{55} + 9q^{56} - 23q^{57} - 29q^{58} - 29q^{59} + 405q^{60} - 174q^{61} - 29q^{62} - 29q^{63} - 210q^{64} - 29q^{65} + 244q^{66} - 75q^{67} - 77q^{68} - 103q^{69} - 115q^{70} - 29q^{71} - 203q^{72} - 79q^{73} + 87q^{74} + 7q^{75} - 105q^{76} + 39q^{77} + 233q^{78} - 29q^{79} + 99q^{80} + 207q^{81} - 29q^{82} + 93q^{83} - 435q^{84} + 126q^{85} - 147q^{86} + 115q^{87} - 139q^{88} - 435q^{89} - 29q^{90} - 57q^{91} - 47q^{92} - 99q^{93} - 51q^{94} + 233q^{95} + 609q^{96} - 29q^{97} + 377q^{98} - 29q^{99} + O(q^{100}) \)

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.h.a \(784\) \(2.787\) None \(-29\) \(-25\) \(-21\) \(-29\)