Properties

Label 22.3.b
Level 22
Weight 3
Character orbit b
Rep. character \(\chi_{22}(21,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(22, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
22.3.b.a \(2\) \(0.599\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(-2\) \(0\) \(q+\beta q^{2}+q^{3}-2q^{4}-q^{5}+\beta q^{6}-6\beta q^{7}+\cdots\)

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

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