Space of modular forms of level 98, weight 7, and Character 98.f

• Label: 98.7.f
• Level: $98$
• Weight: $7$
• Character orbit: 98.f
• Rep. character: $\chi_{98}(13,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $168$
• Newform subspaces: $1$
• Sturm bound: $98$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.f (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(98\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(98, [\chi])\).

	Total	New	Old
Modular forms	516	168	348
Cusp forms	492	168	324
Eisenstein series	24	0	24

Trace form

168 * q - 896 * q^4 + 784 * q^6 - 308 * q^7 + 9884 * q^9 - 3976 * q^11 - 2688 * q^14 - 3948 * q^15 - 28672 * q^16 + 6272 * q^17 + 11200 * q^18 - 25088 * q^20 - 19488 * q^21 + 16800 * q^22 + 81536 * q^23 + 111524 * q^25 - 59584 * q^26 - 23520 * q^27 - 9856 * q^28 - 27916 * q^29 + 21728 * q^30 + 129500 * q^35 + 316288 * q^36 - 92876 * q^37 + 121520 * q^38 + 170240 * q^39 + 150528 * q^40 + 116032 * q^41 + 828352 * q^42 + 18032 * q^43 - 58240 * q^44 - 1894144 * q^45 - 365904 * q^46 - 525476 * q^47 + 702716 * q^49 - 230272 * q^50 + 741720 * q^51 - 784000 * q^52 + 1549800 * q^53 + 571536 * q^54 + 2086224 * q^55 - 179200 * q^56 + 347368 * q^57 - 1683360 * q^58 - 559188 * q^59 - 126336 * q^60 - 94276 * q^61 + 262640 * q^62 + 805980 * q^63 - 917504 * q^64 - 867944 * q^65 + 300832 * q^67 - 738920 * q^69 + 814464 * q^70 - 799792 * q^71 + 358400 * q^72 + 1693440 * q^73 + 40320 * q^74 - 1468236 * q^75 - 1939896 * q^77 + 2300480 * q^78 - 2184560 * q^79 - 3804584 * q^81 + 5372360 * q^83 + 397824 * q^84 + 345240 * q^85 + 1009456 * q^86 - 2590532 * q^87 - 892416 * q^88 - 9698080 * q^89 + 1561728 * q^90 + 2196012 * q^91 - 777728 * q^92 - 1685320 * q^93 - 5809440 * q^94 - 3220672 * q^95 + 2589216 * q^98 - 7151816 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.7.f.a	$98$	$7$	98.f	49.f	$14$	$168$	$28$	$22.545$		None		✓	✓	✓	98.7.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-308\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{7}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(98, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)