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Properties

Label 22.9.b
Level $22$
Weight $9$
Character orbit 22.b
Rep. character $\chi_{22}(21,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $27$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 9 \)
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: \(27\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(22, [\chi])\).

Total New Old
Modular forms 26 8 18
Cusp forms 22 8 14
Eisenstein series 4 0 4

Trace form

\( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9} + O(q^{10}) \) \( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9} + 5808 q^{11} - 23296 q^{12} + 12288 q^{14} + 87958 q^{15} + 131072 q^{16} + 180480 q^{20} + 359040 q^{22} - 802026 q^{23} + 999558 q^{25} - 1321728 q^{26} - 1561354 q^{27} + 196726 q^{31} - 4286722 q^{33} - 701952 q^{34} - 5706496 q^{36} + 8627998 q^{37} + 9288960 q^{38} + 4366848 q^{42} - 743424 q^{44} + 1146988 q^{45} - 14335392 q^{47} + 2981888 q^{48} - 6714712 q^{49} + 55946352 q^{53} - 10078442 q^{55} - 1572864 q^{56} - 23226624 q^{58} + 21793110 q^{59} - 11258624 q^{60} - 16777216 q^{64} - 44242176 q^{66} - 113809034 q^{67} - 171636914 q^{69} + 137817600 q^{70} + 16741974 q^{71} + 346496844 q^{75} - 137074080 q^{77} - 57993216 q^{78} - 23101440 q^{80} + 85282724 q^{81} + 47480832 q^{82} + 49839360 q^{86} - 45957120 q^{88} + 42055422 q^{89} - 146801952 q^{91} + 102659328 q^{92} + 253251118 q^{93} + 100034782 q^{97} - 333541978 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.9.b.a 22.b 11.b $8$ $8.962$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(182\) \(-1410\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(23+\beta _{1})q^{3}-2^{7}q^{4}+(-176+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)