Properties

Label 547.2.m
Level $547$
Weight $2$
Character orbit 547.m
Rep. character $\chi_{547}(10,\cdot)$
Character field $\Q(\zeta_{91})$
Dimension $3168$
Newform subspaces $1$
Sturm bound $91$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.m (of order \(91\) and degree \(72\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 547 \)
Character field: \(\Q(\zeta_{91})\)
Newform subspaces: \( 1 \)
Sturm bound: \(91\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(547, [\chi])\).

Total New Old
Modular forms 3312 3312 0
Cusp forms 3168 3168 0
Eisenstein series 144 144 0

Trace form

\( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} + O(q^{10}) \) \( 3168 q - 76 q^{2} - 38 q^{3} - 34 q^{4} - 75 q^{5} - 42 q^{6} - 60 q^{7} - 77 q^{8} - 550 q^{9} - 91 q^{10} - 61 q^{11} - 31 q^{12} - 72 q^{13} - 21 q^{14} - 46 q^{15} + 24 q^{16} - 91 q^{17} + 9 q^{18} - 89 q^{19} - 108 q^{20} - 81 q^{21} - 50 q^{22} - 86 q^{23} - 33 q^{24} - 15 q^{25} + 137 q^{26} + 163 q^{27} - 47 q^{28} - 12 q^{29} + 29 q^{30} - 53 q^{31} - 122 q^{32} - 21 q^{33} - 80 q^{34} - 75 q^{35} - 8 q^{36} - 49 q^{37} - 47 q^{38} + 128 q^{39} - 246 q^{40} - 686 q^{41} - 466 q^{42} - 9 q^{43} - 43 q^{44} + 156 q^{45} - 91 q^{46} - 72 q^{47} + 21 q^{48} - 8 q^{49} - 84 q^{50} + 93 q^{51} + 4 q^{52} - 32 q^{53} - 71 q^{54} - 34 q^{55} - 263 q^{56} - 61 q^{57} - 36 q^{58} - 23 q^{59} + 87 q^{60} + 38 q^{61} + 26 q^{62} + 133 q^{63} + 343 q^{64} + 143 q^{65} - 65 q^{66} - 50 q^{67} - 213 q^{68} - 140 q^{69} + 372 q^{70} - 75 q^{71} + 147 q^{72} - 18 q^{73} - 85 q^{74} + 97 q^{75} - 47 q^{76} + 11 q^{77} + 55 q^{78} - 37 q^{79} - 142 q^{80} - 532 q^{81} - 94 q^{82} - 279 q^{83} + 395 q^{84} - 75 q^{85} - 147 q^{86} + 84 q^{87} + 345 q^{88} + 8 q^{89} + 278 q^{90} - 38 q^{91} - 78 q^{92} - 83 q^{93} - 540 q^{94} + 35 q^{95} + 123 q^{96} - 735 q^{97} - 90 q^{98} + 351 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(547, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
547.2.m.a 547.m 547.m $3168$ $4.368$ None \(-76\) \(-38\) \(-75\) \(-60\) $\mathrm{SU}(2)[C_{91}]$