Space of modular forms of level 98, weight 2, and Character 98.g

• Label: 98.2.g
• Level: $98$
• Weight: $2$
• Character orbit: 98.g
• Rep. character: $\chi_{98}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(98, [\chi])\).

	Total	New	Old
Modular forms	192	48	144
Cusp forms	144	48	96
Eisenstein series	48	0	48

Trace form

48 * q + 4 * q^4 - 14 * q^6 - 14 * q^9 - 18 * q^11 + 2 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 - 6 * q^22 - 50 * q^23 - 4 * q^25 - 14 * q^26 - 42 * q^27 + 2 * q^29 - 8 * q^30 - 14 * q^35 - 14 * q^36 - 4 * q^37 + 28 * q^38 + 16 * q^39 + 28 * q^40 + 56 * q^41 - 42 * q^42 + 16 * q^43 + 24 * q^44 + 14 * q^45 + 76 * q^46 - 28 * q^47 + 112 * q^49 + 24 * q^50 + 92 * q^51 - 14 * q^52 - 34 * q^53 + 84 * q^54 + 42 * q^55 + 28 * q^56 - 10 * q^57 - 12 * q^58 + 42 * q^59 + 20 * q^60 + 28 * q^62 - 42 * q^63 - 8 * q^64 - 28 * q^65 - 12 * q^67 - 28 * q^68 - 28 * q^69 - 14 * q^70 + 6 * q^71 - 4 * q^72 - 42 * q^73 - 26 * q^74 - 84 * q^75 - 42 * q^77 - 24 * q^78 - 20 * q^79 - 14 * q^80 + 10 * q^81 - 84 * q^83 - 42 * q^84 + 16 * q^85 - 54 * q^86 + 98 * q^87 - 18 * q^88 - 56 * q^89 - 42 * q^90 - 14 * q^91 + 16 * q^92 + 34 * q^93 - 70 * q^94 + 72 * q^95 - 28 * q^97 - 28 * q^98 - 120 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.2.g.a	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		None		✓			98.2.g.a	$2$	$0$	\(-2\)	\(7\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
98.2.g.b	$98$	$2$	98.g	49.g	$21$	$24$	$2$	$0.783$		None		✓			98.2.g.b	$2$	$0$	\(2\)	\(-7\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

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