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Properties

Label 349.2.k
Level $349$
Weight $2$
Character orbit 349.k
Rep. character $\chi_{349}(3,\cdot)$
Character field $\Q(\zeta_{174})$
Dimension $1624$
Newform subspaces $1$
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: \(\Q(\zeta_{174})\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(349, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
349.2.k.a 349.k 349.k $1624$ $2.787$ None \(-55\) \(-58\) \(-60\) \(-58\) $\mathrm{SU}(2)[C_{174}]$