Properties

Label 1.22
Level 1
Weight 22
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q - 288 q^{2} - 128844 q^{3} - 2014208 q^{4} + 21640950 q^{5} + 37107072 q^{6} - 768078808 q^{7} + 1184071680 q^{8} + 6140423133 q^{9} + O(q^{10}) \) \( q - 288 q^{2} - 128844 q^{3} - 2014208 q^{4} + 21640950 q^{5} + 37107072 q^{6} - 768078808 q^{7} + 1184071680 q^{8} + 6140423133 q^{9} - 6232593600 q^{10} - 94724929188 q^{11} + 259518615552 q^{12} - 80621789794 q^{13} + 221206696704 q^{14} - 2788306561800 q^{15} + 3883087691776 q^{16} + 3052282930002 q^{17} - 1768441862304 q^{18} - 7920788351740 q^{19} - 43589374617600 q^{20} + 98962345937952 q^{21} + 27280779606144 q^{22} - 73845437470344 q^{23} - 152560531537920 q^{24} - 8506441300625 q^{25} + 23219075460672 q^{26} + 556597069939080 q^{27} + 1547070479704064 q^{28} - 4253031736469010 q^{29} + 803032289798400 q^{30} + 1900541176310432 q^{31} - 3601507547086848 q^{32} + 12204738776298672 q^{33} - 879057483840576 q^{34} - 16621955079987600 q^{35} - 12368089397873664 q^{36} + 22191429912035222 q^{37} + 2281187045301120 q^{38} + 10387633884218136 q^{39} + 25624436023296000 q^{40} - 20622803144546358 q^{41} - 28501155630130176 q^{42} - 193605854685795844 q^{43} + 190795710169903104 q^{44} + 132884590000096350 q^{45} + 21267485991459072 q^{46} + 146960504315611632 q^{47} - 500312550559186944 q^{48} + 31399191215416857 q^{49} + 2449855094580000 q^{50} - 393268341833177688 q^{51} + 162389053977393152 q^{52} + 2038267110310687206 q^{53} - 160299956142455040 q^{54} - 2049937456311048600 q^{55} - 909460364560957440 q^{56} + 1020546054391588560 q^{57} + 1224873140103074880 q^{58} - 5975882742742352820 q^{59} + 5616229383230054400 q^{60} + 6190617154478149262 q^{61} - 547355858777404416 q^{62} - 4716328880610265464 q^{63} - 7106190945422409728 q^{64} - 1744732121842464300 q^{65} - 3514964767574017536 q^{66} + 16961315295446680052 q^{67} - 6147932695873468416 q^{68} + 9514541545429002336 q^{69} + 4787123063036428800 q^{70} - 5632758963952293528 q^{71} + 7270701135002173440 q^{72} - 43284759511102937494 q^{73} - 6391131814666143936 q^{74} + 1096003922937727500 q^{75} + 15954115264381521920 q^{76} + 72756210698603447904 q^{77} - 2991638558654823168 q^{78} - 51264938664949064560 q^{79} + 84033706583339827200 q^{80} - 135945187666282668519 q^{81} + 5939367305629351104 q^{82} + 48911854702961049156 q^{83} - 199330748886990422016 q^{84} + 66054302274026781900 q^{85} + 55758486149509203072 q^{86} + 547977621053613124440 q^{87} - 112161106041516195840 q^{88} - 504303489899844009030 q^{89} - 38270761920027748800 q^{90} + 61923888203802085552 q^{91} + 148740070916266647552 q^{92} - 244873327320541300608 q^{93} - 42324625242896150016 q^{94} - 171413384680587753000 q^{95} + 464032638396857843712 q^{96} + 808275058155029184482 q^{97} - 9042967070040054816 q^{98} - 581651146457782106004 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.22.a \(\chi_{1}(1, \cdot)\) 1.22.a.a 1 1