Properties

Label 22.9
Level 22
Weight 9
Dimension 40
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 270
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(270\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(22))\).

Total New Old
Modular forms 130 40 90
Cusp forms 110 40 70
Eisenstein series 20 0 20

Trace form

\( 40 q + 4480 q^{6} - 10950 q^{7} + 43180 q^{9} + O(q^{10}) \) \( 40 q + 4480 q^{6} - 10950 q^{7} + 43180 q^{9} - 41790 q^{11} - 44800 q^{12} + 24990 q^{13} + 119040 q^{14} + 361540 q^{15} - 553530 q^{17} + 152320 q^{18} + 442680 q^{19} - 1119090 q^{23} + 573440 q^{24} + 80820 q^{25} - 2104320 q^{26} - 846870 q^{27} + 51200 q^{28} + 2380710 q^{29} + 4488960 q^{30} + 378380 q^{31} - 4915350 q^{33} - 4567040 q^{34} - 12788370 q^{35} - 609280 q^{36} + 1651300 q^{37} + 9273600 q^{38} + 17382010 q^{39} + 3768320 q^{40} + 5153790 q^{41} - 10988800 q^{42} + 2000640 q^{44} + 7101780 q^{45} - 15447040 q^{46} - 27811770 q^{47} + 13181510 q^{49} + 13816320 q^{50} + 37405440 q^{51} + 18368000 q^{52} + 55098930 q^{53} - 57290680 q^{55} - 119710960 q^{57} - 52352000 q^{58} - 27632010 q^{59} + 1451520 q^{60} + 26432690 q^{61} + 64485120 q^{62} + 289643740 q^{63} - 123082240 q^{66} - 247069510 q^{67} - 70851840 q^{68} - 205510690 q^{69} + 86874880 q^{70} + 55046040 q^{71} + 61603840 q^{72} + 208728710 q^{73} + 56355840 q^{74} + 283660920 q^{75} - 44867490 q^{77} - 132981760 q^{78} - 247776110 q^{79} - 45711360 q^{80} - 536990380 q^{81} + 64949760 q^{82} + 434637000 q^{83} + 159336960 q^{84} + 286821150 q^{85} + 42798720 q^{86} + 55541760 q^{88} - 294150030 q^{89} - 270179840 q^{90} - 313809450 q^{91} + 132560640 q^{92} + 318639380 q^{93} + 429944320 q^{94} + 1032904950 q^{95} + 24881350 q^{97} - 792604320 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(22))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
22.9.b \(\chi_{22}(21, \cdot)\) 22.9.b.a 8 1
22.9.d \(\chi_{22}(7, \cdot)\) 22.9.d.a 32 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)