Space of modular forms of level 117, weight 2, and Character 117.l

• Label: 117.2.l
• Level: $117$
• Weight: $2$
• Character orbit: 117.l
• Rep. character: $\chi_{117}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(117, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

24 * q - q^3 - 22 * q^4 - 12 * q^6 - 3 * q^7 + q^9 - 4 * q^10 - 11 * q^12 - 2 * q^13 - 6 * q^14 - 9 * q^15 + 14 * q^16 + 6 * q^17 + 30 * q^18 - 9 * q^19 - 27 * q^20 - 15 * q^21 + 14 * q^22 + 9 * q^23 + 30 * q^24 + 2 * q^25 + 14 * q^27 + 36 * q^29 + 18 * q^30 - 12 * q^31 + 9 * q^33 + 6 * q^34 - 24 * q^35 - 28 * q^36 - 3 * q^37 + 24 * q^38 + 7 * q^39 + 16 * q^40 - 15 * q^41 - 21 * q^42 - 3 * q^43 - 3 * q^45 - 6 * q^46 + 3 * q^47 - 13 * q^48 + 3 * q^49 + 12 * q^50 + 21 * q^51 - 20 * q^52 - 12 * q^53 + 3 * q^54 - 7 * q^55 - 6 * q^56 - 45 * q^57 + 9 * q^60 + 8 * q^61 + 15 * q^62 - 63 * q^63 - 26 * q^64 - 66 * q^65 + 30 * q^66 - 24 * q^67 - 66 * q^68 + 33 * q^69 - 15 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^74 - 2 * q^75 + 21 * q^76 + 48 * q^77 + 5 * q^79 + 90 * q^80 + 37 * q^81 + 5 * q^82 + 51 * q^83 + 69 * q^84 + 42 * q^86 - 6 * q^87 + 10 * q^88 - 3 * q^89 + 21 * q^90 + 6 * q^91 - 6 * q^92 + 24 * q^93 + 35 * q^94 - 27 * q^96 + 105 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(117, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.2.l.a	$117$	$2$	117.l	117.l	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		✓			117.2.l.a	$2$	$0$	\(0\)	\(0\)	\(3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
117.2.l.b	$117$	$2$	117.l	117.l	$6$	$22$	$11$	$0.934$		None		✓	✓		117.2.l.b	$2$	$0$	\(0\)	\(-1\)	\(-3\)	\(-6\)		$\mathrm{SU}(2)[C_{6}]$