Space of modular forms of level 97, weight 7, and Character 97.j

• Label: 97.7.j
• Level: $97$
• Weight: $7$
• Character orbit: 97.j
• Rep. character: $\chi_{97}(19,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $768$
• Newform subspaces: $1$
• Sturm bound: $57$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	97.j (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 97 \)
Character field:			\(\Q(\zeta_{32})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(57\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(97, [\chi])\).

	Total	New	Old
Modular forms	800	800	0
Cusp forms	768	768	0
Eisenstein series	32	32	0

Trace form

768 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 11056 * q^9 - 16 * q^10 - 16 * q^11 - 15376 * q^12 - 16 * q^13 - 16 * q^14 + 7408 * q^15 - 16 * q^16 + 16624 * q^17 - 16 * q^18 - 16 * q^19 - 147472 * q^20 - 16 * q^21 - 16 * q^22 - 58256 * q^23 - 16 * q^24 + 137264 * q^25 - 154016 * q^26 - 16 * q^27 + 341984 * q^28 + 89840 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 340752 * q^33 - 52816 * q^34 - 32 * q^35 + 847424 * q^37 - 16 * q^38 + 115440 * q^39 - 193552 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 2273056 * q^44 + 876912 * q^45 - 16 * q^46 - 1005328 * q^47 + 2408544 * q^48 - 16 * q^49 - 16 * q^50 - 1161232 * q^51 - 737296 * q^52 - 16 * q^53 + 3867760 * q^54 + 1343984 * q^55 - 16 * q^56 - 16 * q^57 - 16 * q^58 - 289296 * q^59 + 2993744 * q^60 - 32 * q^61 + 2794224 * q^63 - 16 * q^64 - 75472 * q^65 - 4970384 * q^66 - 16 * q^67 + 2374640 * q^68 - 16 * q^69 - 7989680 * q^70 - 712336 * q^71 + 1008 * q^72 + 1935344 * q^73 - 2283856 * q^74 - 16 * q^75 - 11887216 * q^76 - 16 * q^77 - 16 * q^78 - 1386128 * q^79 + 2523120 * q^80 - 10341296 * q^81 + 5814464 * q^82 - 1431056 * q^83 - 6469648 * q^84 + 3728000 * q^85 - 2123536 * q^86 - 13733072 * q^87 + 5529584 * q^88 + 2929904 * q^89 + 24516400 * q^90 + 7856624 * q^91 + 11070784 * q^92 - 9253456 * q^93 + 3202544 * q^94 + 5163504 * q^95 - 2227216 * q^97 + 9243296 * q^98 - 6220816 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(97, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
97.7.j.a	$97$	$7$	97.j	97.j	$32$	$768$	$48$	$22.315$		None		✓	✓	✓	97.7.j.a	$2$	$0$	\(-16\)	\(-16\)	\(-16\)	\(-16\)		$\mathrm{SU}(2)[C_{32}]$