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Properties

Label 211.2.d
Level $211$
Weight $2$
Character orbit 211.d
Rep. character $\chi_{211}(55,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $64$
Newform subspaces $2$
Sturm bound $35$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 211.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 211 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(35\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 72 72 0
Cusp forms 64 64 0
Eisenstein series 8 8 0

Trace form

\( 64 q - 4 q^{3} - 10 q^{4} - 3 q^{5} + 13 q^{6} - 10 q^{7} - 3 q^{8} - 30 q^{9} + O(q^{10}) \) \( 64 q - 4 q^{3} - 10 q^{4} - 3 q^{5} + 13 q^{6} - 10 q^{7} - 3 q^{8} - 30 q^{9} - 4 q^{10} - 9 q^{11} - 32 q^{12} + 7 q^{13} + 8 q^{14} - 14 q^{15} - 2 q^{16} + 9 q^{17} - 4 q^{18} - 38 q^{19} + 15 q^{20} - 3 q^{21} + 29 q^{22} + 17 q^{23} + 25 q^{24} - 7 q^{25} - 36 q^{26} + 8 q^{27} - 75 q^{28} + 5 q^{29} + 55 q^{30} - 20 q^{31} - 46 q^{32} - 28 q^{33} + 56 q^{34} - 4 q^{35} + 61 q^{36} - 26 q^{37} - 44 q^{38} + 55 q^{39} + 86 q^{40} + 43 q^{41} + 46 q^{42} - 104 q^{43} + 54 q^{44} - 16 q^{45} - 93 q^{46} + 16 q^{47} + 33 q^{48} - 36 q^{49} - 40 q^{50} + 53 q^{51} + 38 q^{52} + 14 q^{53} - 50 q^{54} + 2 q^{55} + 19 q^{56} - 4 q^{57} + 24 q^{58} - 7 q^{59} + 6 q^{60} + 23 q^{61} - 103 q^{62} - 40 q^{63} + 21 q^{64} - 29 q^{65} - 25 q^{66} - 2 q^{67} + 60 q^{68} - 14 q^{69} - 65 q^{70} - 18 q^{71} + 39 q^{72} + 38 q^{73} + 15 q^{74} - 18 q^{75} - 72 q^{76} + 58 q^{77} + 32 q^{78} + 45 q^{79} + 60 q^{80} - 38 q^{81} - 107 q^{82} + 43 q^{83} - 85 q^{84} - 19 q^{85} + 35 q^{86} + 3 q^{87} + 68 q^{88} + 3 q^{89} + 144 q^{90} - 4 q^{91} - 44 q^{92} - 31 q^{93} + 112 q^{94} + 12 q^{95} - 44 q^{96} - 7 q^{97} + 28 q^{98} - 73 q^{99} + O(q^{100}) \)

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.d.a 211.d 211.d $4$ $1.685$ \(\Q(\zeta_{10})\) None \(2\) \(1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2})q^{2}-\zeta_{10}^{2}q^{3}+(-1+\cdots)q^{4}+\cdots\)
211.2.d.b 211.d 211.d $60$ $1.685$ None \(-2\) \(-5\) \(-2\) \(-12\) $\mathrm{SU}(2)[C_{5}]$