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

• Label: 98.4.e
• Level: $98$
• Weight: $4$
• Character orbit: 98.e
• Rep. character: $\chi_{98}(15,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $84$
• 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.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{7})\)
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	264	84	180
Cusp forms	240	84	156
Eisenstein series	24	0	24

Trace form

\( 84 q - 6 q^{3} - 56 q^{4} + 26 q^{5} - 8 q^{6} - 56 q^{9} + O(q^{10}) \)

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.e.a	$98$	$4$	98.e	49.e	$7$	$42$	$7$	$5.782$		None		$2$	$0$	\(-14\)	\(-5\)	\(12\)	\(-7\)		$\mathrm{SU}(2)[C_{7}]$
98.4.e.b	$98$	$4$	98.e	49.e	$7$	$42$	$7$	$5.782$		None		$2$	$0$	\(14\)	\(-1\)	\(14\)	\(7\)		$\mathrm{SU}(2)[C_{7}]$

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

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