Space of modular forms of level 116, weight 1, and Character 116.j

• Label: 116.1.j
• Level: $116$
• Weight: $1$
• Character orbit: 116.j
• Rep. character: $\chi_{116}(7,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	116.j (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(116, [\chi])\).

	Total	New	Old
Modular forms	18	18	0
Cusp forms	6	6	0
Eisenstein series	12	12	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

6 * q - q^2 - q^4 - 2 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - 2 * q^17 - q^18 + 5 * q^20 - 3 * q^25 + 5 * q^26 - q^29 - q^32 + 5 * q^34 - q^36 - 2 * q^37 + 5 * q^40 - 2 * q^41 + 5 * q^45 - q^49 - 3 * q^50 - 2 * q^52 + 5 * q^53 - q^58 - 2 * q^61 - q^64 + 3 * q^65 - 2 * q^68 - q^72 + 5 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 4 * q^85 - 2 * q^89 - 2 * q^90 + 5 * q^97 - q^98

Decomposition of \(S_{1}^{\mathrm{new}}(116, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	\(\Q(\zeta_{14})\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	116.1.j.a	$4$	$0$	\(-1\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots\)