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

• Label: 117.2.ba
• Level: $117$
• Weight: $2$
• Character orbit: 117.ba
• Rep. character: $\chi_{117}(71,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.ba (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	72	16	56
Cusp forms	40	16	24
Eisenstein series	32	0	32

Trace form

\( 16 q + 4 q^{7} + O(q^{10}) \)

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.ba.a	$117$	$2$	117.ba	39.k	$12$	$8$	$2$	$0.934$	\(\Q(\zeta_{24})\)	None		✓			117.2.ba.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{24}^{4}-\zeta_{24}^{5})q^{2}-2\zeta_{24}q^{4}+(\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
117.2.ba.b	$117$	$2$	117.ba	39.k	$12$	$8$	$2$	$0.934$	\(\Q(\zeta_{24})\)	None		✓			117.2.ba.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}^{7}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}+2\zeta_{24}^{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(117, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(117, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)