Space of modular forms of level 279, weight 2, and Character 279.r

• Label: 279.2.r
• Level: $279$
• Weight: $2$
• Character orbit: 279.r
• Rep. character: $\chi_{279}(68,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 279 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(279, [\chi])\).

	Total	New	Old
Modular forms	68	68	0
Cusp forms	60	60	0
Eisenstein series	8	8	0

Trace form

60 * q - 6 * q^2 - 3 * q^3 + 26 * q^4 - 6 * q^5 + 6 * q^6 - 5 * q^9 - 4 * q^10 - 6 * q^11 + 6 * q^12 - 3 * q^13 + 3 * q^15 - 22 * q^16 - 4 * q^18 - 4 * q^19 - 15 * q^22 + 9 * q^23 + 36 * q^24 + 26 * q^25 - 18 * q^26 + 9 * q^27 + 4 * q^28 - 3 * q^30 + q^31 + 6 * q^32 - 27 * q^33 + 3 * q^34 + 18 * q^36 - 15 * q^37 + 27 * q^38 + 9 * q^39 - 8 * q^40 + 9 * q^41 - 39 * q^42 + 9 * q^43 - 18 * q^44 - 52 * q^45 - 9 * q^47 + 3 * q^48 - 18 * q^49 - 30 * q^51 + 42 * q^53 - 15 * q^55 - 72 * q^56 + 3 * q^57 - 9 * q^58 - 30 * q^60 + 21 * q^61 - 45 * q^62 - 43 * q^63 - 26 * q^64 + 36 * q^65 - 24 * q^66 + 5 * q^67 - 60 * q^68 + 27 * q^69 + 13 * q^70 + 9 * q^71 - 89 * q^72 + 15 * q^73 - 33 * q^74 + 18 * q^75 - 46 * q^76 - 18 * q^78 - 6 * q^79 + 33 * q^80 - 5 * q^81 - 22 * q^82 + 18 * q^83 - 6 * q^84 - 15 * q^85 + 42 * q^86 + 66 * q^87 - 36 * q^89 + 31 * q^90 - 36 * q^92 - 66 * q^93 - 28 * q^94 + 39 * q^95 - 6 * q^96 - 6 * q^97 + 177 * q^98 - 21 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(279, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
279.2.r.a	$279$	$2$	279.r	279.r	$6$	$60$	$30$	$2.228$		None		✓	✓	✓	279.2.o.a	$2$	$0$	\(-6\)	\(-3\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$