Space of modular forms of level 98, weight 4, and Character 98.g

• Label: 98.4.g
• Level: $98$
• Weight: $4$
• Character orbit: 98.g
• Rep. character: $\chi_{98}(9,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $168$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(56\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(98, [\chi])\).

	Total	New	Old
Modular forms	528	168	360
Cusp forms	480	168	312
Eisenstein series	48	0	48

Trace form

\( 168 q - 6 q^{3} + 56 q^{4} - 2 q^{5} + 44 q^{6} + 48 q^{7} + 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.4.g.a	$98$	$4$	98.g	49.g	$21$	$84$	$7$	$5.782$		None		$2$	$0$	\(-14\)	\(-8\)	\(7\)	\(20\)		$\mathrm{SU}(2)[C_{21}]$
98.4.g.b	$98$	$4$	98.g	49.g	$21$	$84$	$7$	$5.782$		None		$2$	$0$	\(14\)	\(2\)	\(-9\)	\(28\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{4}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)