Properties

Label 2.22
Level 2
Weight 22
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(2))\).

Total New Old
Modular forms 6 2 4
Cusp forms 4 2 2
Eisenstein series 2 0 2

Trace form

\( 2 q + 130920 q^{3} + 2097152 q^{4} - 23718420 q^{5} - 12582912 q^{6} + 574223440 q^{7} - 12275185734 q^{9} + O(q^{10}) \) \( 2 q + 130920 q^{3} + 2097152 q^{4} - 23718420 q^{5} - 12582912 q^{6} + 574223440 q^{7} - 12275185734 q^{9} + 34477178880 q^{10} - 20036715336 q^{11} + 137279569920 q^{12} - 1045474008260 q^{13} + 2335363301376 q^{14} - 1759470846480 q^{15} + 2199023255552 q^{16} - 7946413934940 q^{17} - 1647354839040 q^{18} + 34056523599880 q^{19} - 24870565969920 q^{20} + 23576486574144 q^{21} - 198143052349440 q^{22} + 275998560315120 q^{23} - 13194139533312 q^{24} - 105587771970850 q^{25} + 763057026367488 q^{26} - 2163118970450160 q^{27} + 602116917821440 q^{28} + 1648319193086940 q^{29} + 2406099525304320 q^{30} - 4025217119435456 q^{31} - 122745071797920 q^{33} - 14808624685645824 q^{34} + 31583536312739040 q^{35} - 12871465156214784 q^{36} + 18166192255567660 q^{37} - 12296613569495040 q^{38} - 73015070738904528 q^{39} + 36151942321274880 q^{40} + 21101722895757204 q^{41} + 149260180201144320 q^{42} - 157459727760364040 q^{43} - 21010018820161536 q^{44} + 118491491854692540 q^{45} - 17400697687375872 q^{46} - 642515922620105760 q^{47} + 143948062308433920 q^{48} + 1648407099408845874 q^{49} - 817744209090969600 q^{50} - 431320508067297456 q^{51} - 1096258953685237760 q^{52} + 1470670856960699340 q^{53} + 101014647015997440 q^{54} - 3019852165744949040 q^{55} + 2448805909103640576 q^{56} + 2303119716265115040 q^{57} + 3191216599172382720 q^{58} - 6736451234462070120 q^{59} - 1844938902318612480 q^{60} + 364336743223117084 q^{61} + 2322545873591992320 q^{62} - 5358824269905078000 q^{63} + 2305843009213693952 q^{64} + 24943153326978577320 q^{65} - 12844384093873373184 q^{66} - 13954116530216070680 q^{67} - 8332418938243645440 q^{68} + 18171269944352010432 q^{69} - 17796761688326799360 q^{70} + 4322530771479236304 q^{71} - 1727376747701207040 q^{72} + 11112960893524425940 q^{73} + 45152071124533641216 q^{74} - 2005310298666023400 q^{75} + 35710853290267770880 q^{76} - 226402501182977528640 q^{77} + 56527266668127191040 q^{78} + 133177052109561844000 q^{79} - 26078678582474833920 q^{80} - 13801077277696652238 q^{81} - 72015436582087557120 q^{82} + 207172716519439614600 q^{83} + 24721737985969618944 q^{84} - 149215598230637549160 q^{85} - 111936012458259382272 q^{86} + 88751674784436796080 q^{87} - 207768049260366397440 q^{88} + 77778919424044267380 q^{89} - 192070560187479490560 q^{90} + 549563307151695419744 q^{91} + 289405466380987269120 q^{92} - 277425987879796903680 q^{93} + 263647117032718073856 q^{94} - 606039792323431352400 q^{95} - 13835058055282163712 q^{96} - 1296645454449453731900 q^{97} + 1341020348565883453440 q^{98} + 278622531605875217112 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.22.a \(\chi_{2}(1, \cdot)\) 2.22.a.a 1 1
2.22.a.b 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 1}\)