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

• Label: 98.7.d
• Level: $98$
• Weight: $7$
• Character orbit: 98.d
• Rep. character: $\chi_{98}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $98$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
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	184	40	144
Cusp forms	152	40	112
Eisenstein series	32	0	32

Trace form

40 * q - 640 * q^4 + 336 * q^5 + 5908 * q^9 + 2016 * q^10 + 780 * q^11 - 42360 * q^15 - 20480 * q^16 + 17304 * q^17 + 8032 * q^18 + 32004 * q^19 - 43104 * q^22 + 20408 * q^23 - 10752 * q^24 + 66160 * q^25 + 4704 * q^26 + 62696 * q^29 - 30160 * q^30 + 3108 * q^31 - 3276 * q^33 - 378112 * q^36 - 145364 * q^37 - 155568 * q^38 + 264476 * q^39 - 64512 * q^40 - 173456 * q^43 + 24960 * q^44 + 172116 * q^45 + 334704 * q^46 - 313908 * q^47 + 444352 * q^50 - 370212 * q^51 - 255360 * q^52 - 973860 * q^53 - 386064 * q^54 - 1000712 * q^57 + 513024 * q^58 + 835464 * q^59 + 677760 * q^60 + 995316 * q^61 + 1310720 * q^64 + 387996 * q^65 - 1673280 * q^66 + 547808 * q^67 - 553728 * q^68 - 15808 * q^71 + 257024 * q^72 + 1617084 * q^73 + 714912 * q^74 + 2042208 * q^75 - 2738560 * q^78 - 2389432 * q^79 - 344064 * q^80 - 3700848 * q^81 - 66528 * q^82 + 2161128 * q^85 + 176800 * q^86 + 2057076 * q^87 + 689664 * q^88 - 739116 * q^89 - 1306112 * q^92 + 4362396 * q^93 - 3795120 * q^94 - 1272920 * q^95 + 344064 * q^96 + 14832872 * 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.d.a	$98$	$7$	98.d	7.d	$6$	$8$	$4$	$22.545$	8.0.339738624.1	None		✓			98.7.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-4\beta _{2}-4\beta _{6})q^{2}+(11\beta _{3}-10\beta _{5}+\cdots)q^{3}+\cdots\)
98.7.d.b	$98$	$7$	98.d	7.d	$6$	$8$	$4$	$22.545$	8.0.\(\cdots\).14	None					14.7.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2^{5}+2^{5}\beta _{1})q^{4}+\cdots\)
98.7.d.c	$98$	$7$	98.d	7.d	$6$	$8$	$4$	$22.545$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None					14.7.d.a	$2$	$0$	\(0\)	\(0\)	\(336\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{2}q^{2}+(-\beta _{2}-\beta _{3}+\beta _{4}+\beta _{6})q^{3}+\cdots\)
98.7.d.d	$98$	$7$	98.d	7.d	$6$	$16$	$8$	$22.545$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		98.7.b.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{4}\cdot 7^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q+4\beta _{4}q^{2}+(-2\beta _{3}+2\beta _{8}-\beta _{10})q^{3}+\cdots\)

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

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