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Properties

Label 22.9.d
Level $22$
Weight $9$
Character orbit 22.d
Rep. character $\chi_{22}(7,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $32$
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.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
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 104 32 72
Cusp forms 88 32 56
Eisenstein series 16 0 16

Trace form

\( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9} + O(q^{10}) \) \( 32 q - 182 q^{3} + 1024 q^{4} + 1410 q^{5} + 4480 q^{6} - 10950 q^{7} - 1402 q^{9} - 47598 q^{11} - 21504 q^{12} + 24990 q^{13} + 106752 q^{14} + 273582 q^{15} - 131072 q^{16} - 553530 q^{17} + 152320 q^{18} + 442680 q^{19} - 180480 q^{20} - 359040 q^{22} - 317064 q^{23} + 573440 q^{24} - 918738 q^{25} - 782592 q^{26} + 714484 q^{27} + 51200 q^{28} + 2380710 q^{29} + 4488960 q^{30} + 181654 q^{31} - 628628 q^{33} - 3865088 q^{34} - 12788370 q^{35} + 5097216 q^{36} - 6976698 q^{37} - 15360 q^{38} + 17382010 q^{39} + 3768320 q^{40} + 5153790 q^{41} - 15355648 q^{42} + 2744064 q^{44} + 5954792 q^{45} - 15447040 q^{46} - 13476378 q^{47} - 2981888 q^{48} + 19896222 q^{49} + 13816320 q^{50} + 37405440 q^{51} + 18368000 q^{52} - 847422 q^{53} - 47212238 q^{55} + 1572864 q^{56} - 119710960 q^{57} - 29125376 q^{58} - 49425120 q^{59} + 12710144 q^{60} + 26432690 q^{61} + 64485120 q^{62} + 289643740 q^{63} + 16777216 q^{64} - 78840064 q^{66} - 133260476 q^{67} - 70851840 q^{68} - 33873776 q^{69} - 50942720 q^{70} + 38304066 q^{71} + 61603840 q^{72} + 208728710 q^{73} + 56355840 q^{74} - 62835924 q^{75} + 92206590 q^{77} - 74988544 q^{78} - 247776110 q^{79} - 22609920 q^{80} - 622273104 q^{81} + 17468928 q^{82} + 434637000 q^{83} + 159336960 q^{84} + 286821150 q^{85} - 7040640 q^{86} + 101498880 q^{88} - 336205452 q^{89} - 270179840 q^{90} - 167007498 q^{91} + 29901312 q^{92} + 65388262 q^{93} + 429944320 q^{94} + 1032904950 q^{95} - 75153432 q^{97} - 459062342 q^{99} + O(q^{100}) \)

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.d.a 22.d 11.d $32$ $8.962$ None \(0\) \(-182\) \(1410\) \(-10950\) $\mathrm{SU}(2)[C_{10}]$

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

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