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Properties

Label 22.2.c
Level $22$
Weight $2$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $4$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(22, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 4 4 0
Eisenstein series 16 0 16

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.2.c.a 22.c 11.c $4$ $0.176$ \(\Q(\zeta_{10})\) None \(-1\) \(-4\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\zeta_{10}q^{2}+(-1+\zeta_{10}-\zeta_{10}^{3})q^{3}+\cdots\)