Space of modular forms of level 98, weight 3, and Character 98.b

• Label: 98.3.b
• Level: $98$
• Weight: $3$
• Character orbit: 98.b
• Rep. character: $\chi_{98}(97,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $42$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(42\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(98, [\chi])\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	20	8	12
Eisenstein series	16	0	16

Trace form

\( 8 q + 16 q^{4} - 28 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(98, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.3.b.a	$98$	$3$	98.b	7.b	$2$	$4$	$4$	$2.670$	4.0.2048.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(2\beta _{1}+2\beta _{3})q^{3}+2q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots\)
98.3.b.b	$98$	$3$	98.b	7.b	$2$	$4$	$4$	$2.670$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+2q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)