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

• Label: 98.8.e
• Level: $98$
• Weight: $8$
• Character orbit: 98.e
• Rep. character: $\chi_{98}(15,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $204$
• 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.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
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	600	204	396
Cusp forms	576	204	372
Eisenstein series	24	0	24

Trace form

204 * q + 54 * q^3 - 2176 * q^4 + 246 * q^5 + 2752 * q^6 - 1016 * q^7 - 31472 * q^9 + 2416 * q^10 - 22338 * q^11 + 3456 * q^12 + 970 * q^13 + 2640 * q^14 - 28002 * q^15 - 139264 * q^16 - 119290 * q^17 - 4544 * q^18 + 36952 * q^19 + 16640 * q^20 - 86966 * q^21 - 124048 * q^22 + 181298 * q^23 - 31744 * q^24 - 643770 * q^25 - 230752 * q^26 + 978486 * q^27 - 65024 * q^28 + 448810 * q^29 - 353152 * q^30 - 423164 * q^31 + 789776 * q^33 + 270944 * q^34 - 623644 * q^35 - 2014208 * q^36 - 1584080 * q^37 - 869152 * q^38 - 1690958 * q^39 + 61440 * q^40 + 1156492 * q^41 + 2181632 * q^42 - 774972 * q^43 + 978816 * q^44 + 8884658 * q^45 - 1295408 * q^46 + 3613252 * q^47 - 1327104 * q^48 - 5651038 * q^49 - 2787648 * q^50 + 3454320 * q^51 + 829056 * q^52 + 5093314 * q^53 + 3195632 * q^54 + 3575360 * q^55 + 2183168 * q^56 - 7635786 * q^57 + 773280 * q^58 - 2904396 * q^59 - 1792128 * q^60 - 26051060 * q^61 + 7057616 * q^62 + 3470718 * q^63 - 8912896 * q^64 + 3682504 * q^65 + 3578240 * q^66 - 1898564 * q^67 - 10719488 * q^68 - 17955180 * q^69 + 9942688 * q^70 - 688974 * q^71 - 290816 * q^72 - 9381322 * q^73 + 11908880 * q^74 + 5563270 * q^75 + 8510592 * q^76 + 9631566 * q^77 + 6809792 * q^78 - 5171332 * q^79 - 6160384 * q^80 - 38336852 * q^81 - 4020192 * q^82 + 31287570 * q^83 + 12951808 * q^84 + 59079032 * q^85 + 4845264 * q^86 + 35375586 * q^87 + 2096128 * q^88 + 3608024 * q^89 + 6840224 * q^90 - 23860028 * q^91 - 9398272 * q^92 + 42348626 * q^93 - 3114416 * q^94 - 75830184 * q^95 - 2031616 * q^96 - 48396632 * q^97 + 1682080 * 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.e.a	$98$	$8$	98.e	49.e	$7$	$102$	$17$	$30.614$		None		✓			98.8.e.a	$2$	$0$	\(-136\)	\(199\)	\(274\)	\(-343\)		$\mathrm{SU}(2)[C_{7}]$
98.8.e.b	$98$	$8$	98.e	49.e	$7$	$102$	$17$	$30.614$		None		✓			98.8.e.b	$2$	$0$	\(136\)	\(-145\)	\(-28\)	\(-673\)		$\mathrm{SU}(2)[C_{7}]$

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

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