Space of modular forms of level 98, weight 8, and Character 98.g

• Label: 98.8.g
• Level: $98$
• Weight: $8$
• Character orbit: 98.g
• Rep. character: $\chi_{98}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $384$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.g (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(112\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(98, [\chi])\).

	Total	New	Old
Modular forms	1200	384	816
Cusp forms	1152	384	768
Eisenstein series	48	0	48

Trace form

384 * q + 2048 * q^4 - 252 * q^5 - 1456 * q^6 + 1680 * q^7 + 27902 * q^9 - 1792 * q^10 + 29382 * q^11 - 24080 * q^13 + 24192 * q^14 + 28002 * q^15 + 131072 * q^16 + 6622 * q^17 - 2272 * q^18 + 52570 * q^19 + 31360 * q^20 + 261884 * q^21 + 124048 * q^22 - 401570 * q^23 - 57344 * q^24 + 443740 * q^25 + 321328 * q^26 - 394674 * q^27 + 53760 * q^28 - 448810 * q^29 - 176576 * q^30 - 236264 * q^31 + 282100 * q^33 + 200704 * q^34 + 680554 * q^35 - 2558080 * q^36 + 1428612 * q^37 - 2786336 * q^38 - 5833000 * q^39 - 301056 * q^40 + 3541832 * q^41 + 3586576 * q^42 - 1439632 * q^43 + 1506816 * q^44 - 6605690 * q^45 - 3808288 * q^46 - 13735036 * q^47 - 11957848 * q^49 + 2787648 * q^50 + 708828 * q^51 + 794752 * q^52 + 6737858 * q^53 + 12937120 * q^54 + 19203058 * q^55 + 2996224 * q^56 + 6085230 * q^57 - 7681056 * q^58 - 11328030 * q^59 - 8044800 * q^60 - 6739824 * q^61 - 4253984 * q^62 + 33754014 * q^63 - 16777216 * q^64 + 1841252 * q^65 - 5411840 * q^66 - 3398204 * q^67 + 3508736 * q^68 + 9650340 * q^69 - 24306352 * q^70 + 688974 * q^71 - 145408 * q^72 + 8378034 * q^73 - 5276528 * q^74 + 20194076 * q^75 + 5562368 * q^76 + 5383266 * q^77 - 6809792 * q^78 - 11257980 * q^79 + 6135808 * q^80 + 5678858 * q^81 - 15697920 * q^82 - 94694292 * q^83 - 26927488 * q^84 - 59079032 * q^85 - 29174640 * q^86 + 25803666 * q^87 + 3746816 * q^88 + 106350916 * q^89 + 61160848 * q^90 + 100582426 * q^91 + 9398272 * q^92 - 72366218 * q^93 - 18554032 * q^94 - 92373216 * q^95 - 3670016 * q^96 - 71601236 * q^97 - 33320224 * q^98 + 163460072 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.8.g.a	$98$	$8$	98.g	49.g	$21$	$192$	$16$	$30.614$		None		✓			98.8.g.a	$2$	$0$	\(-128\)	\(259\)	\(-14\)	\(1848\)		$\mathrm{SU}(2)[C_{21}]$
98.8.g.b	$98$	$8$	98.g	49.g	$21$	$192$	$16$	$30.614$		None		✓			98.8.g.b	$2$	$0$	\(128\)	\(-259\)	\(-238\)	\(-168\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{8}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(98, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)