Space of modular forms of level 152, weight 1, and Character 152.k

• Label: 152.1.k
• Level: $152$
• Weight: $1$
• Character orbit: 152.k
• Rep. character: $\chi_{152}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	152.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(152, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^8 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - q^19 + q^22 + q^24 - q^25 + 2 * q^27 - q^32 - q^33 - 2 * q^34 + 2 * q^38 + q^41 - 2 * q^43 + q^44 + q^48 + 2 * q^49 + 2 * q^50 + 2 * q^51 - q^54 - 2 * q^57 + q^59 + 2 * q^64 - q^66 + q^67 + 4 * q^68 + q^73 - 2 * q^75 - q^76 + q^81 + q^82 - 2 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 + q^97 - q^98

Decomposition of \(S_{1}^{\mathrm{new}}(152, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-2}) \)	None		✓	✓	✓	152.1.k.a	$4$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)