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

• Label: 197.2.e
• Level: $197$
• Weight: $2$
• Character orbit: 197.e
• Rep. character: $\chi_{197}(6,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $33$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 197 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(33\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	108	108	0
Cusp forms	96	96	0
Eisenstein series	12	12	0

Trace form

96 * q - 7 * q^2 - 7 * q^3 + 23 * q^4 - 7 * q^5 - 18 * q^6 + 5 * q^7 - 21 * q^8 + 11 * q^9 + 3 * q^10 - 21 * q^11 - 21 * q^12 - 7 * q^13 + 14 * q^15 - 9 * q^16 - 7 * q^17 - 28 * q^18 - 28 * q^19 - 7 * q^21 + 31 * q^22 - 15 * q^23 - 33 * q^24 - 3 * q^25 + 15 * q^26 - 49 * q^27 - 38 * q^28 + 8 * q^29 - 126 * q^30 + 21 * q^31 + 7 * q^32 + 20 * q^33 + 45 * q^34 - 7 * q^35 + 226 * q^36 - 42 * q^37 - 21 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 - 16 * q^42 + 6 * q^43 + 21 * q^44 + 7 * q^45 + 7 * q^46 - 28 * q^47 - 91 * q^48 - 5 * q^49 + 133 * q^50 - 5 * q^51 - 98 * q^52 - 5 * q^53 - 64 * q^54 + 13 * q^55 + 70 * q^56 + 70 * q^57 + 21 * q^58 + 11 * q^59 - 59 * q^60 - 25 * q^61 + 13 * q^62 + 2 * q^63 - 25 * q^64 + 34 * q^65 - 112 * q^66 + 63 * q^67 - 22 * q^70 + 56 * q^71 + 7 * q^73 + 7 * q^74 + 42 * q^75 + 62 * q^76 - 133 * q^78 - 91 * q^79 + 21 * q^80 - 39 * q^81 - 7 * q^82 - 14 * q^83 + 123 * q^85 + 84 * q^86 + 20 * q^88 - 77 * q^89 - 133 * q^90 + 77 * q^91 + 51 * q^92 - 52 * q^93 + 161 * q^94 - 133 * q^95 + 60 * q^96 - 25 * q^97 + 14 * q^98 - 63 * 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.e.a	$197$	$2$	197.e	197.e	$14$	$6$	$1$	$1.573$	\(\Q(\zeta_{14})\)	None		✓			197.2.e.a	$2$	$0$	\(0\)	\(-7\)	\(7\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{5})q^{3}+\cdots\)
197.2.e.b	$197$	$2$	197.e	197.e	$14$	$90$	$15$	$1.573$		None		✓	✓		197.2.e.b	$2$	$0$	\(-7\)	\(0\)	\(-14\)	\(6\)		$\mathrm{SU}(2)[C_{14}]$