Space of modular forms of level 8 and weight 22

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

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 - 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

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

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