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

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

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

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