Space of modular forms of level 163, weight 2, and Character 163.e

• Label: 163.2.e
• Level: $163$
• Weight: $2$
• Character orbit: 163.e
• Rep. character: $\chi_{163}(38,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $27$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	163.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 163 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(27\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(163, [\chi])\).

	Total	New	Old
Modular forms	84	84	0
Cusp forms	72	72	0
Eisenstein series	12	12	0

Trace form

72 * q - 3 * q^2 - 3 * q^4 - 9 * q^6 + 6 * q^7 + 21 * q^8 + 6 * q^9 - 21 * q^11 - 33 * q^12 + 3 * q^13 + 18 * q^14 - 36 * q^15 + 21 * q^16 + 9 * q^17 - 66 * q^18 - 24 * q^19 + 42 * q^20 - 3 * q^21 - 6 * q^22 - 60 * q^23 + 15 * q^24 - 24 * q^25 + 9 * q^26 + 6 * q^27 + 9 * q^28 - 24 * q^29 + 6 * q^30 - 9 * q^31 - 12 * q^32 - 21 * q^33 - 27 * q^34 - 6 * q^35 - 12 * q^36 - 9 * q^37 - 12 * q^38 - 12 * q^39 + 84 * q^40 + 30 * q^42 + 21 * q^43 + 27 * q^44 + 3 * q^45 - 63 * q^46 + 15 * q^47 + 12 * q^48 + 48 * q^49 - 48 * q^50 + 18 * q^51 - 21 * q^52 + 18 * q^53 + 72 * q^54 + 42 * q^55 - 75 * q^56 + 6 * q^57 + 42 * q^58 - 48 * q^59 - 126 * q^60 - 36 * q^61 - 6 * q^62 + 6 * q^63 + 21 * q^64 + 57 * q^65 + 84 * q^66 + 15 * q^67 + 6 * q^68 + 42 * q^69 - 99 * q^70 + 15 * q^71 - 39 * q^72 - 48 * q^73 - 81 * q^74 - 3 * q^75 - 60 * q^76 - 87 * q^77 + 216 * q^78 + 51 * q^79 + 60 * q^80 - 57 * q^81 - 81 * q^82 + 42 * q^83 + 81 * q^84 + 102 * q^85 + 39 * q^86 + 27 * q^87 - 42 * q^88 - 45 * q^89 + 216 * q^90 + 21 * q^91 - 72 * q^92 + 105 * q^93 - 75 * q^94 + 24 * q^95 - 111 * q^96 + 60 * q^97 - 9 * q^98 - 3 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(163, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
163.2.e.a	$163$	$2$	163.e	163.e	$9$	$72$	$12$	$1.302$		None		✓	✓	✓	163.2.e.a	$2$	$0$	\(-3\)	\(0\)	\(0\)	\(6\)		$\mathrm{SU}(2)[C_{9}]$