Space of modular forms of level 1, weight 22, and trivial character

• Label: 1.22.a
• Level: $1$
• Weight: $22$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $1$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(1))\).

	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 - 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

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.22.a.a	$1$	$22$	1.a	1.a	$1$	$1$	$1$	$2.795$	\(\Q\)	None	✓	✓	✓	✓	1.22.a.a	$1$	$1$	\(-288\)	\(-128844\)	\(21640950\)	\(-768078808\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-288q^{2}-128844q^{3}-2014208q^{4}+\cdots\)