Space of modular forms of level 152, weight 3, and Character 152.g

• Label: 152.3.g
• Level: $152$
• Weight: $3$
• Character orbit: 152.g
• Rep. character: $\chi_{152}(37,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $3$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(152, [\chi])\).

	Total	New	Old
Modular forms	42	42	0
Cusp forms	38	38	0
Eisenstein series	4	4	0

Trace form

\( 38 q + 2 q^{4} - 22 q^{6} - 4 q^{7} + 98 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.3.g.a	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	\(\Q(\sqrt{-38}) \)	✓	$2$	$0$	\(-6\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.b	$152$	$3$	152.g	152.g	$2$	$3$	$3$	$4.142$	3.3.4104.1	\(\Q(\sqrt{-38}) \)	✓	$2$	$0$	\(6\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.c	$152$	$3$	152.g	152.g	$2$	$32$	$32$	$4.142$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{2}]$