Properties

Label 22.3.b
Level $22$
Weight $3$
Character orbit 22.b
Rep. character $\chi_{22}(21,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 22.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(22, [\chi])\).

Total New Old
Modular forms 8 2 6
Cusp forms 4 2 2
Eisenstein series 4 0 4

Trace form

\( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{3} - 4 q^{4} - 2 q^{5} - 16 q^{9} + 14 q^{11} - 4 q^{12} + 24 q^{14} - 2 q^{15} + 8 q^{16} + 4 q^{20} - 24 q^{22} + 34 q^{23} - 48 q^{25} - 24 q^{26} - 34 q^{27} + 34 q^{31} + 14 q^{33} - 72 q^{34} + 32 q^{36} + 94 q^{37} + 72 q^{38} + 24 q^{42} - 28 q^{44} + 16 q^{45} - 116 q^{47} + 8 q^{48} - 46 q^{49} + 4 q^{53} - 14 q^{55} - 48 q^{56} + 96 q^{58} - 110 q^{59} + 4 q^{60} - 16 q^{64} - 24 q^{66} + 178 q^{67} + 34 q^{69} - 24 q^{70} - 14 q^{71} - 48 q^{75} + 144 q^{77} - 24 q^{78} - 8 q^{80} + 110 q^{81} - 24 q^{82} - 48 q^{86} + 48 q^{88} - 194 q^{89} + 144 q^{91} - 68 q^{92} + 34 q^{93} - 242 q^{97} - 112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.3.b.a 22.b 11.b $2$ $0.599$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)