Space of modular forms of level 116, weight 6, and Character 116.i

• Label: 116.6.i
• Level: $116$
• Weight: $6$
• Character orbit: 116.i
• Rep. character: $\chi_{116}(5,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $90$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	116.i (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(90\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(116, [\chi])\).

	Total	New	Old
Modular forms	468	72	396
Cusp forms	432	72	360
Eisenstein series	36	0	36

Trace form

\( 72 q + 10 q^{5} - 76 q^{7} + 650 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(116, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
116.6.i.a	$116$	$6$	116.i	29.e	$14$	$72$	$12$	$18.605$		None		✓	✓	✓	116.6.i.a	$2$	$0$	\(0\)	\(0\)	\(10\)	\(-76\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{6}^{\mathrm{old}}(116, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(116, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)