Space of modular forms of level 197, weight 2, and Character 197.g

• Label: 197.2.g
• Level: $197$
• Weight: $2$
• Character orbit: 197.g
• Rep. character: $\chi_{197}(16,\cdot)$
• Character field: $\Q(\zeta_{49})$
• Dimension: $630$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.g (of order \(49\) and degree \(42\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{49})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(197, [\chi])\).

	Total	New	Old
Modular forms	714	714	0
Cusp forms	630	630	0
Eisenstein series	84	84	0

Trace form

630 * q - 42 * q^2 - 42 * q^3 - 28 * q^4 - 42 * q^5 - 21 * q^6 - 28 * q^7 - 28 * q^8 - 42 * q^9 - 28 * q^10 - 28 * q^11 - 28 * q^12 - 42 * q^13 - 28 * q^14 - 154 * q^15 - 42 * q^17 - 21 * q^18 - 7 * q^19 - 35 * q^20 - 42 * q^21 - 42 * q^23 + 28 * q^24 - 42 * q^25 - 7 * q^26 + 42 * q^27 - 49 * q^28 - 182 * q^29 + 77 * q^30 - 14 * q^31 - 28 * q^32 + 35 * q^33 - 14 * q^34 - 42 * q^35 + 84 * q^36 + 14 * q^37 - 28 * q^38 - 21 * q^39 + 28 * q^40 - 28 * q^41 - 112 * q^42 - 56 * q^43 - 210 * q^44 + 49 * q^45 - 7 * q^47 + 42 * q^48 + 42 * q^49 + 98 * q^50 - 14 * q^51 + 49 * q^52 - 42 * q^53 + 63 * q^54 - 161 * q^56 - 175 * q^57 - 42 * q^58 + 42 * q^59 + 126 * q^60 - 14 * q^61 + 42 * q^62 + 49 * q^63 + 98 * q^64 + 56 * q^65 + 175 * q^66 + 28 * q^67 + 273 * q^68 - 7 * q^69 - 252 * q^70 - 77 * q^71 - 364 * q^72 - 28 * q^73 + 35 * q^74 + 7 * q^75 + 133 * q^76 + 21 * q^77 + 210 * q^78 + 42 * q^79 - 14 * q^80 - 14 * q^81 - 42 * q^82 + 161 * q^83 - 245 * q^84 - 266 * q^85 - 147 * q^86 - 35 * q^87 + 77 * q^88 + 28 * q^89 + 315 * q^90 + 154 * q^91 + 84 * q^92 - 7 * q^93 + 182 * q^94 + 126 * q^95 + 245 * q^96 + 42 * q^97 - 308 * q^98 - 161 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(197, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
197.2.g.a	$197$	$2$	197.g	197.g	$49$	$630$	$15$	$1.573$		None		✓	✓	✓	197.2.g.a	$2$	$0$	\(-42\)	\(-42\)	\(-42\)	\(-28\)		$\mathrm{SU}(2)[C_{49}]$