Properties

Label 349.2.k
Level 349
Weight 2
Character orbit k
Rep. character \(\chi_{349}(3,\cdot)\)
Character field \(\Q(\zeta_{174})\)
Dimension 1624
Newforms 1
Sturm bound 58
Trace bound 0

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Defining parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.k (of order \(174\) and degree \(56\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 349 \)
Character field: \(\Q(\zeta_{174})\)
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 1736 1736 0
Cusp forms 1624 1624 0
Eisenstein series 112 112 0

Trace form

\( 1624q - 55q^{2} - 58q^{3} - 85q^{4} - 60q^{5} - 58q^{6} - 58q^{7} - 145q^{8} - 29q^{9} + O(q^{10}) \) \( 1624q - 55q^{2} - 58q^{3} - 85q^{4} - 60q^{5} - 58q^{6} - 58q^{7} - 145q^{8} - 29q^{9} - 58q^{10} - 58q^{11} - 57q^{12} - 55q^{13} - 48q^{14} - 59q^{15} - 29q^{16} - 48q^{17} + 43q^{18} + 67q^{19} - 58q^{20} + 58q^{21} - 55q^{22} - 41q^{23} - 39q^{24} - 29q^{25} - 112q^{26} - 76q^{27} - 58q^{28} - 56q^{29} - 67q^{30} - 90q^{31} - 67q^{32} - 46q^{33} + 5q^{34} - 82q^{36} + 45q^{37} - 58q^{38} - 58q^{39} - 112q^{40} + 10q^{41} + 305q^{42} - 13q^{43} + 40q^{44} - 56q^{45} - 85q^{46} - 58q^{47} - 122q^{48} - 93q^{49} - 441q^{50} - 160q^{51} + 58q^{52} - 58q^{53} - 85q^{54} + 34q^{55} - 69q^{56} - 29q^{57} - 58q^{58} - 40q^{59} + 522q^{60} + 87q^{61} - 49q^{62} - 37q^{63} + 335q^{64} - 58q^{65} - 565q^{66} - 116q^{67} - 58q^{68} + 16q^{69} - 98q^{70} - 34q^{71} + 44q^{72} - 52q^{73} - 204q^{74} - 95q^{76} - 54q^{77} + 439q^{78} - 58q^{79} - 192q^{80} - 209q^{81} - 79q^{82} + 162q^{83} + 330q^{84} - 192q^{85} + 126q^{86} - 190q^{87} - 8q^{88} + 345q^{89} - 46q^{90} - 30q^{91} + 62q^{92} - 89q^{93} - 87q^{94} - 350q^{95} + 990q^{96} - 43q^{97} - 464q^{98} - 97q^{99} + O(q^{100}) \)

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.k.a \(1624\) \(2.787\) None \(-55\) \(-58\) \(-60\) \(-58\)