Space of modular forms of level 8, weight 24, and Character 8.b

• Label: 8.24.b
• Level: $8$
• Weight: $24$
• Character orbit: 8.b
• Rep. character: $\chi_{8}(5,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(8, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	22	22	0
Eisenstein series	2	2	0

Trace form

22 * q + 966 * q^2 - 2692748 * q^4 + 808474636 * q^6 - 3954653488 * q^7 - 62449515288 * q^8 - 627621192182 * q^9 + 306551586824 * q^10 + 4738963291912 * q^12 + 2554976858640 * q^14 + 34787309795152 * q^15 + 125154838417936 * q^16 - 56302527224628 * q^17 + 446161586227418 * q^18 + 1636886471059632 * q^20 - 4623700128159460 * q^22 - 11015984418588816 * q^23 - 18078206734516336 * q^24 - 46585599340209474 * q^25 + 27250717788149592 * q^26 + 138692994088916960 * q^28 - 488911498998255472 * q^30 - 115035310661977792 * q^31 - 891944197477352544 * q^32 - 130381876864731720 * q^33 - 37114294427523156 * q^34 - 393476445326922420 * q^36 + 59766494286016044 * q^38 - 7306343944537941392 * q^39 + 3119814657858702944 * q^40 - 873679648968660804 * q^41 - 13169379704798110688 * q^42 - 6267968004734939544 * q^44 + 39910612351228940592 * q^46 + 31671536615597195232 * q^47 + 64384452337720605600 * q^48 + 93779014951766063430 * q^49 + 23545355465402880174 * q^50 + 69932399231188294032 * q^52 - 254652912328971096904 * q^54 + 116128086218437548304 * q^55 - 326396860069627787328 * q^56 - 114894185664348581416 * q^57 + 237757612882123831544 * q^58 + 152791833194214275808 * q^60 - 110982742264658693568 * q^62 - 747046720288436989904 * q^63 - 346989846701397864896 * q^64 - 1053855950458512730080 * q^65 - 203911725430162137864 * q^66 - 3258039087878785432920 * q^68 + 2968764652284013667008 * q^70 + 899640501832912828752 * q^71 + 2946373220645509576856 * q^72 + 559359934400329544444 * q^73 - 9923101491310112330424 * q^74 + 428624541380213056968 * q^76 - 2471266213285303462864 * q^78 + 22902810108576674238752 * q^79 - 3782040353719193722944 * q^80 + 19941890002286730208094 * q^81 + 36453020970218011543452 * q^82 + 45141182808204460944064 * q^84 - 15886127162249675082660 * q^86 - 81382390546507918310736 * q^87 - 3908545514801450803120 * q^88 - 22088427411999876708708 * q^89 - 12341073929354165265544 * q^90 - 67328764866606494559840 * q^92 - 38580870001427880584352 * q^94 + 92033426911960620850896 * q^95 + 4721260650938050323008 * q^96 - 110707211645456005315348 * q^97 - 164747394499232111265162 * q^98

Decomposition of \(S_{24}^{\mathrm{new}}(8, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
8.24.b.a	$8$	$24$	8.b	8.b	$2$	$22$	$22$	$26.816$		None		✓	✓	✓	8.24.b.a	$2$	$0$	\(966\)	\(0\)	\(0\)	\(-3954653488\)		$\mathrm{SU}(2)[C_{2}]$