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Properties

Label 211.2.f
Level $211$
Weight $2$
Character orbit 211.f
Rep. character $\chi_{211}(58,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $96$
Newform subspaces $1$
Sturm bound $35$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 211.f (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 211 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(35\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(211, [\chi])\).

Total New Old
Modular forms 108 108 0
Cusp forms 96 96 0
Eisenstein series 12 12 0

Trace form

\( 96 q - 9 q^{2} - q^{3} - 19 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} + 13 q^{8} - 7 q^{9} + O(q^{10}) \) \( 96 q - 9 q^{2} - q^{3} - 19 q^{4} - 5 q^{5} - 3 q^{6} + 3 q^{7} + 13 q^{8} - 7 q^{9} - 2 q^{10} + 9 q^{11} + 10 q^{12} + 5 q^{13} + 4 q^{14} - 26 q^{15} - 65 q^{16} + 34 q^{18} - 10 q^{19} - q^{20} - 66 q^{21} - q^{22} - 62 q^{23} + 22 q^{24} - 23 q^{25} + 27 q^{26} + 20 q^{27} - 7 q^{28} - 33 q^{29} - 14 q^{30} - 23 q^{31} + 13 q^{32} + 55 q^{33} + 45 q^{34} + 24 q^{35} - 38 q^{36} + 20 q^{37} + 25 q^{38} - 15 q^{39} - 21 q^{40} + 27 q^{41} + 7 q^{42} - 49 q^{43} - 50 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} + 95 q^{48} + 5 q^{49} - 27 q^{50} - 10 q^{51} + 28 q^{52} + 4 q^{53} + 3 q^{54} + 12 q^{55} - 29 q^{57} - 53 q^{58} - 10 q^{59} + 13 q^{60} - 100 q^{61} - 98 q^{62} + 27 q^{63} + 57 q^{64} + 18 q^{65} + 47 q^{66} - 10 q^{67} + 103 q^{68} + 58 q^{69} - 17 q^{70} - 18 q^{71} - 23 q^{72} - 98 q^{73} - 4 q^{74} + 100 q^{75} - 57 q^{76} - 36 q^{77} + 97 q^{78} + 59 q^{79} - 3 q^{80} - 21 q^{81} + 28 q^{83} - 123 q^{84} - 85 q^{85} + 2 q^{86} + 11 q^{87} + 53 q^{88} + 61 q^{89} + 30 q^{90} + 13 q^{91} - 63 q^{92} + 83 q^{93} - 55 q^{94} - 73 q^{95} - 29 q^{96} + 73 q^{97} + 22 q^{98} + 11 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(211, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
211.2.f.a 211.f 211.f $96$ $1.685$ None \(-9\) \(-1\) \(-5\) \(3\) $\mathrm{SU}(2)[C_{7}]$