Properties

Label 349.2.i
Level $349$
Weight $2$
Character orbit 349.i
Rep. character $\chi_{349}(9,\cdot)$
Character field $\Q(\zeta_{87})$
Dimension $1568$
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.i (of order \(87\) and degree \(56\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 349 \)
Character field: \(\Q(\zeta_{87})\)
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 1680 1680 0
Cusp forms 1568 1568 0
Eisenstein series 112 112 0

Trace form

\( 1568 q - 58 q^{2} - 58 q^{3} - 28 q^{4} - 62 q^{5} - 72 q^{6} - 60 q^{7} + 23 q^{8} - 30 q^{9} + O(q^{10}) \) \( 1568 q - 58 q^{2} - 58 q^{3} - 28 q^{4} - 62 q^{5} - 72 q^{6} - 60 q^{7} + 23 q^{8} - 30 q^{9} - 56 q^{10} - 56 q^{11} - 69 q^{12} - 56 q^{13} - 60 q^{14} - 67 q^{15} - 24 q^{16} - 58 q^{17} + 40 q^{18} - 169 q^{19} - 72 q^{20} + 46 q^{21} - 51 q^{22} - 47 q^{23} + q^{24} - 52 q^{25} + 11 q^{26} - 28 q^{27} - 6 q^{28} - 66 q^{29} - 37 q^{30} - 10 q^{31} - 52 q^{32} - 70 q^{33} - 44 q^{34} - 42 q^{35} - 124 q^{36} - 159 q^{37} - 118 q^{38} - 32 q^{39} - 82 q^{40} - 403 q^{42} - 35 q^{43} + 78 q^{44} - 76 q^{45} - 63 q^{46} - 32 q^{47} + 22 q^{48} - 32 q^{49} + 308 q^{50} + 44 q^{51} + 255 q^{52} - 46 q^{53} - 51 q^{54} + 48 q^{55} - 39 q^{56} - 83 q^{57} - 46 q^{58} - 42 q^{59} - 742 q^{60} + 190 q^{61} - 31 q^{62} - 89 q^{63} + 149 q^{64} - 130 q^{65} + 385 q^{66} - 24 q^{67} - q^{68} + 48 q^{69} - 6 q^{70} - 48 q^{71} + 243 q^{72} - 81 q^{73} + 75 q^{74} - 32 q^{75} - 67 q^{76} - 48 q^{77} - 547 q^{78} - 106 q^{79} + 148 q^{80} + 418 q^{81} - 50 q^{82} - 304 q^{83} + 338 q^{84} + 90 q^{85} - 46 q^{86} + 102 q^{87} - 116 q^{88} + 340 q^{89} - 126 q^{90} - 112 q^{91} - 106 q^{92} - q^{93} - 91 q^{94} + 120 q^{95} - 914 q^{96} - 58 q^{97} + 316 q^{98} - 131 q^{99} + O(q^{100}) \)

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.i.a 349.i 349.i $1568$ $2.787$ None \(-58\) \(-58\) \(-62\) \(-60\) $\mathrm{SU}(2)[C_{87}]$