Properties

Label 22.10
Level 22
Weight 10
Dimension 43
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 300
Trace bound 1

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Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(300\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(22))\).

Total New Old
Modular forms 145 43 102
Cusp forms 125 43 82
Eisenstein series 20 0 20

Trace form

\( 43 q - 32 q^{2} + 312 q^{3} - 512 q^{4} - 1740 q^{5} - 2608 q^{6} + 20964 q^{7} - 8192 q^{8} - 826 q^{9} + O(q^{10}) \) \( 43 q - 32 q^{2} + 312 q^{3} - 512 q^{4} - 1740 q^{5} - 2608 q^{6} + 20964 q^{7} - 8192 q^{8} - 826 q^{9} + 72160 q^{10} + 86848 q^{11} - 109568 q^{12} - 592308 q^{13} + 191904 q^{14} + 1500050 q^{15} - 131072 q^{16} - 1160986 q^{17} - 18256 q^{18} - 1615585 q^{19} - 445440 q^{20} + 3592596 q^{21} + 898368 q^{22} - 1600018 q^{23} - 667648 q^{24} + 3579190 q^{25} + 3486592 q^{26} - 1028085 q^{27} - 5756416 q^{28} - 7225850 q^{29} + 2327520 q^{30} - 1759774 q^{31} + 3145728 q^{32} + 21368317 q^{33} + 8457984 q^{34} - 31667610 q^{35} - 11259136 q^{36} - 40833436 q^{37} - 19941280 q^{38} + 57949808 q^{39} + 25681920 q^{40} + 90274006 q^{41} - 40259104 q^{42} - 257053758 q^{43} - 8209152 q^{44} + 287054030 q^{45} + 84581952 q^{46} - 5497946 q^{47} + 20447232 q^{48} - 268814504 q^{49} - 72082080 q^{50} + 95941921 q^{51} - 44919808 q^{52} - 51916288 q^{53} + 265092480 q^{54} + 489080710 q^{55} + 7798784 q^{56} + 110213205 q^{57} - 220349760 q^{58} - 1014956905 q^{59} - 185149440 q^{60} - 165631344 q^{61} - 222624544 q^{62} + 320968072 q^{63} - 33554432 q^{64} + 1707724000 q^{65} + 981560512 q^{66} + 461067484 q^{67} - 297212416 q^{68} - 2169418272 q^{69} - 365796480 q^{70} - 1270828504 q^{71} - 336879616 q^{72} - 1083320038 q^{73} + 163352704 q^{74} + 2825282755 q^{75} + 172147200 q^{76} + 2854050794 q^{77} + 1667383168 q^{78} - 1314056800 q^{79} - 300154880 q^{80} - 4085104407 q^{81} - 2373973264 q^{82} - 877744243 q^{83} - 694590464 q^{84} + 3393806740 q^{85} + 2211682192 q^{86} + 4626309400 q^{87} + 1009573888 q^{88} + 1057716470 q^{89} - 1252699680 q^{90} - 4695303514 q^{91} - 2280158208 q^{92} - 12494755006 q^{93} - 1433112896 q^{94} + 5303189960 q^{95} + 327155712 q^{96} + 8547931169 q^{97} + 5412970416 q^{98} + 7327021414 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(22))\)

We only show spaces with even 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
22.10.a \(\chi_{22}(1, \cdot)\) 22.10.a.a 1 1
22.10.a.b 1
22.10.a.c 1
22.10.a.d 2
22.10.a.e 2
22.10.c \(\chi_{22}(3, \cdot)\) 22.10.c.a 16 4
22.10.c.b 20

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(22))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(22)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)