Properties

Label 8.22
Level 8
Weight 22
Dimension 25
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 88
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(88\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(8))\).

Total New Old
Modular forms 45 27 18
Cusp forms 39 25 14
Eisenstein series 6 2 4

Trace form

\( 25 q + 286 q^{2} - 8668 q^{3} + 409876 q^{4} - 22003634 q^{5} + 118236748 q^{6} + 1305710568 q^{7} + 3649699336 q^{8} - 32845074403 q^{9} + O(q^{10}) \) \( 25 q + 286 q^{2} - 8668 q^{3} + 409876 q^{4} - 22003634 q^{5} + 118236748 q^{6} + 1305710568 q^{7} + 3649699336 q^{8} - 32845074403 q^{9} - 51269339528 q^{10} + 13471294636 q^{11} + 65316900136 q^{12} - 356632250986 q^{13} - 1924309104464 q^{14} - 4148652035976 q^{15} + 7793508571920 q^{16} + 2944582099330 q^{17} - 41325344023822 q^{18} + 55090597707316 q^{19} - 78999934156016 q^{20} + 63483640028832 q^{21} + 294957216952508 q^{22} + 119782518223032 q^{23} + 786737698607504 q^{24} - 1478428301815153 q^{25} - 2772669922448408 q^{26} + 3014062843435496 q^{27} - 4284340177681888 q^{28} + 3202555900321062 q^{29} + 3807691030523312 q^{30} - 6432413120227936 q^{31} - 9127378177656544 q^{32} - 1399279116426112 q^{33} + 19124803780998044 q^{34} + 7975251928887216 q^{35} + 39378114498954828 q^{36} - 26458703887352466 q^{37} - 41860137429498580 q^{38} + 208723224768779736 q^{39} - 160007944946664288 q^{40} - 314607531211763270 q^{41} + 178614544452770272 q^{42} + 231195720126249164 q^{43} - 27785097292304568 q^{44} - 859998337885344938 q^{45} + 184220935820050448 q^{46} + 455529113876298864 q^{47} + 1509829480382701344 q^{48} - 919681508380782479 q^{49} - 1722157324053237098 q^{50} + 5114029246370682760 q^{51} - 1640429312330235856 q^{52} - 4194423668594372354 q^{53} + 785391046636854392 q^{54} + 5356749987096127656 q^{55} - 3751496032099552448 q^{56} - 9611769830660056224 q^{57} + 3182351472522780872 q^{58} + 10009049496232751836 q^{59} + 2751731248604508192 q^{60} - 13732181343142521274 q^{61} - 13336157978726113600 q^{62} + 27233757417227638792 q^{63} - 9021637553716933568 q^{64} - 17209694118604260892 q^{65} + 5291575090585638744 q^{66} + 881069099479908964 q^{67} + 40891724357029299816 q^{68} - 26426991957433856032 q^{69} + 18077776609913587392 q^{70} + 64759972342205966120 q^{71} + 49841566955976579512 q^{72} - 52469598513563931686 q^{73} - 42953490504627871688 q^{74} - 26746902752653120100 q^{75} - 206966483397015363224 q^{76} + 139184164190911890912 q^{77} + 163869164384378609168 q^{78} - 501230898304915178992 q^{79} - 49904712513208125120 q^{80} + 522207510789265924929 q^{81} + 112698322843931711404 q^{82} - 317800628207406564748 q^{83} + 178681601993395676224 q^{84} + 367067042098068889852 q^{85} - 523293212085532715396 q^{86} + 132784063676370258072 q^{87} - 124028902608265335088 q^{88} + 387464901611296280746 q^{89} + 171098967229297148360 q^{90} - 887770236365977512720 q^{91} + 827091233447044225632 q^{92} + 1575602859006642094720 q^{93} - 165060487582514765280 q^{94} - 3156046112971245625640 q^{95} - 715448174391177540544 q^{96} + 468895545392024054674 q^{97} + 137273120368488603630 q^{98} + 817207776598242539644 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.22.a \(\chi_{8}(1, \cdot)\) 8.22.a.a 2 1
8.22.a.b 3
8.22.b \(\chi_{8}(5, \cdot)\) 8.22.b.a 20 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 1}\)