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

• Label: 197.2.b
• Level: $197$
• Weight: $2$
• Character orbit: 197.b
• Rep. character: $\chi_{197}(196,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q\)
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	18	18	0
Cusp forms	16	16	0
Eisenstein series	2	2	0

Trace form

16 * q - 16 * q^4 - 10 * q^6 + 2 * q^7 - 18 * q^9 + 4 * q^10 + 14 * q^15 + 16 * q^16 - 14 * q^19 + 4 * q^22 + 8 * q^23 + 40 * q^24 - 4 * q^25 - 22 * q^26 - 32 * q^28 + 20 * q^29 - 20 * q^33 - 24 * q^34 + 26 * q^36 - 14 * q^37 + 6 * q^39 + 2 * q^40 - 14 * q^41 + 2 * q^42 + 22 * q^43 - 14 * q^47 - 2 * q^49 + 26 * q^51 - 2 * q^53 + 78 * q^54 + 22 * q^55 - 18 * q^59 - 74 * q^60 - 10 * q^61 - 6 * q^62 - 58 * q^63 - 10 * q^64 + 50 * q^65 + 50 * q^70 + 50 * q^76 + 4 * q^81 - 4 * q^85 + 64 * q^88 - 112 * q^90 - 100 * q^92 + 10 * q^93 - 60 * q^96 + 18 * q^97

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.b.a	$197$	$2$	197.b	197.b	$2$	$16$	$16$	$1.573$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	197.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-1+\beta _{2})q^{4}-\beta _{10}q^{5}+\cdots\)