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Properties

Label 211.2.l
Level $211$
Weight $2$
Character orbit 211.l
Rep. character $\chi_{211}(5,\cdot)$
Character field $\Q(\zeta_{35})$
Dimension $384$
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.l (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 211 \)
Character field: \(\Q(\zeta_{35})\)
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 432 432 0
Cusp forms 384 384 0
Eisenstein series 48 48 0

Trace form

\( 384 q - 21 q^{2} - 24 q^{3} - 11 q^{4} - 25 q^{5} - 27 q^{6} - 18 q^{7} - 18 q^{8} + 2 q^{9} + O(q^{10}) \) \( 384 q - 21 q^{2} - 24 q^{3} - 11 q^{4} - 25 q^{5} - 27 q^{6} - 18 q^{7} - 18 q^{8} + 2 q^{9} - 3 q^{10} - 19 q^{11} + 25 q^{12} - 35 q^{13} - 64 q^{14} - 154 q^{15} - 75 q^{16} - 30 q^{17} - 24 q^{18} + 45 q^{19} - 29 q^{20} + 66 q^{21} - 29 q^{22} + 32 q^{23} - 32 q^{24} - 7 q^{25} + 8 q^{26} - 15 q^{27} + 47 q^{28} - 47 q^{29} - 76 q^{30} - 22 q^{31} + 32 q^{32} - 70 q^{34} + 11 q^{35} + 23 q^{36} + 5 q^{37} + 30 q^{38} + 15 q^{39} + 26 q^{40} - 57 q^{41} - 67 q^{42} + 34 q^{43} + 30 q^{44} - 61 q^{45} + 16 q^{46} - 100 q^{47} - 5 q^{48} + 50 q^{49} + 117 q^{50} + 10 q^{51} - 3 q^{52} - 14 q^{53} + 162 q^{54} - 2 q^{55} - 110 q^{56} - 66 q^{57} + 18 q^{58} + 35 q^{59} - 48 q^{60} - 30 q^{61} - 107 q^{62} + 68 q^{63} + 28 q^{64} + 57 q^{65} + 53 q^{66} + 65 q^{67} - 88 q^{68} + 7 q^{69} + 2 q^{70} - 87 q^{71} - 207 q^{72} + 88 q^{73} + 34 q^{74} - 150 q^{75} + 142 q^{76} - 149 q^{77} - 32 q^{78} - 59 q^{79} + 38 q^{80} + 136 q^{81} + 240 q^{82} - 43 q^{83} + 183 q^{84} - 65 q^{85} - 112 q^{86} + 39 q^{87} + 72 q^{88} - 31 q^{89} - 95 q^{90} - 108 q^{91} - 152 q^{92} + 87 q^{93} + 70 q^{94} + 163 q^{95} + 254 q^{96} + 7 q^{97} - 147 q^{98} - 151 q^{99} + O(q^{100}) \)

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.l.a 211.l 211.l $384$ $1.685$ None \(-21\) \(-24\) \(-25\) \(-18\) $\mathrm{SU}(2)[C_{35}]$