Space of modular forms of level 98, weight 7, and Character 98.b

• Label: 98.7.b
• Level: $98$
• Weight: $7$
• Character orbit: 98.b
• Rep. character: $\chi_{98}(97,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $98$
• Trace bound: $9$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(98, [\chi])\).

	Total	New	Old
Modular forms	92	20	72
Cusp forms	76	20	56
Eisenstein series	16	0	16

Trace form

20 * q + 640 * q^4 - 7756 * q^9 + 5016 * q^11 - 3288 * q^15 + 20480 * q^16 + 8768 * q^18 - 10464 * q^22 - 56864 * q^23 - 30124 * q^25 + 34456 * q^29 + 62752 * q^30 - 248192 * q^36 + 174680 * q^37 - 573848 * q^39 - 190720 * q^43 + 160512 * q^44 - 174432 * q^46 - 123232 * q^50 - 41304 * q^51 + 446760 * q^53 - 68008 * q^57 + 496992 * q^58 - 105216 * q^60 + 655360 * q^64 - 1689912 * q^65 - 761840 * q^67 + 538768 * q^71 + 280576 * q^72 + 1424736 * q^74 - 2109824 * q^78 + 226432 * q^79 + 2775756 * q^81 + 4293816 * q^85 + 2730944 * q^86 - 334848 * q^88 - 1819648 * q^92 - 5334360 * q^93 + 737840 * q^95 + 6435400 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(98, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
98.7.b.a	$98$	$7$	98.b	7.b	$2$	$4$	$4$	$22.545$	4.0.2048.2	None		✓			98.7.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-4\beta _{2}q^{2}+(11\beta _{1}+10\beta _{3})q^{3}+2^{5}q^{4}+\cdots\)
98.7.b.b	$98$	$7$	98.b	7.b	$2$	$8$	$8$	$22.545$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓			98.7.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+2^{5}q^{4}+\cdots\)
98.7.b.c	$98$	$7$	98.b	7.b	$2$	$8$	$8$	$22.545$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					14.7.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}\cdot 3^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{3}q^{3}+2^{5}q^{4}+(-4\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

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