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

• Label: 117.2.t
• Level: $117$
• Weight: $2$
• Character orbit: 117.t
• Rep. character: $\chi_{117}(25,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 117 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

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 - 4 * q^3 + 8 * q^4 + 4 * q^9 - 16 * q^10 + 10 * q^12 - 2 * q^13 - 18 * q^14 - 4 * q^16 - 24 * q^17 - 10 * q^22 + 18 * q^23 + 2 * q^25 - 12 * q^26 - 22 * q^27 - 54 * q^30 + 36 * q^35 + 26 * q^36 + 12 * q^38 - 14 * q^39 - 8 * q^40 + 6 * q^42 + 6 * q^43 + 38 * q^48 - 60 * q^51 + 4 * q^52 + 72 * q^53 - 28 * q^55 + 36 * q^56 - 16 * q^61 - 72 * q^62 + 40 * q^64 + 78 * q^66 + 36 * q^68 + 90 * q^69 - 42 * q^74 - 8 * q^75 - 30 * q^77 + 66 * q^78 - 16 * q^79 + 28 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 24 * q^91 - 96 * q^92 + 20 * q^94 + 48 * q^95

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.t.a	$117$	$2$	117.t	117.t	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		✓			117.2.t.a	$2$	$1$	\(0\)	\(-3\)	\(-6\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(-2+\cdots)q^{5}+\cdots\)
117.2.t.b	$117$	$2$	117.t	117.t	$6$	$2$	$1$	$0.934$	\(\Q(\sqrt{-3}) \)	None		✓			117.2.t.a	$2$	$0$	\(0\)	\(-3\)	\(6\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+(2+\cdots)q^{5}+\cdots\)
117.2.t.c	$117$	$2$	117.t	117.t	$6$	$20$	$10$	$0.934$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		117.2.t.c	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{17}q^{2}+\beta _{10}q^{3}+(1-\beta _{6}+\beta _{11}+\cdots)q^{4}+\cdots\)