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

• Label: 98.2.c
• Level: $98$
• Weight: $2$
• Character orbit: 98.c
• Rep. character: $\chi_{98}(67,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	44	8	36
Cusp forms	12	8	4
Eisenstein series	32	0	32

Trace form

8 * q - 4 * q^4 + 4 * q^11 - 16 * q^15 - 4 * q^16 + 4 * q^18 - 8 * q^22 + 8 * q^23 + 4 * q^25 - 16 * q^29 + 8 * q^30 - 24 * q^37 - 16 * q^39 + 40 * q^43 + 4 * q^44 + 8 * q^46 + 32 * q^50 + 20 * q^51 - 8 * q^53 + 24 * q^57 - 16 * q^58 + 8 * q^60 + 8 * q^64 - 16 * q^67 - 48 * q^71 + 4 * q^72 - 16 * q^74 - 32 * q^78 - 8 * q^79 + 32 * q^81 - 16 * q^85 + 12 * q^86 + 4 * q^88 - 16 * q^92 + 8 * q^93 + 40 * q^95 + 8 * 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.c.a	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	\(\Q(\sqrt{-3}) \)	None					14.2.a.a	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
98.2.c.b	$98$	$2$	98.c	7.c	$3$	$2$	$1$	$0.783$	\(\Q(\sqrt{-3}) \)	None					14.2.a.a	$2$	$0$	\(1\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
98.2.c.c	$98$	$2$	98.c	7.c	$3$	$4$	$2$	$0.783$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓		98.2.a.b	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+(2\beta _{1}+\cdots)q^{5}+\cdots\)

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

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