Space of modular forms of level 152, weight 4, and Character 152.b

• Label: 152.4.b
• Level: $152$
• Weight: $4$
• Character orbit: 152.b
• Rep. character: $\chi_{152}(75,\cdot)$
• Character field: $\Q$
• Dimension: $58$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(152, [\chi])\).

	Total	New	Old
Modular forms	62	62	0
Cusp forms	58	58	0
Eisenstein series	4	4	0

Trace form

\( 58 q - 14 q^{4} + 2 q^{6} - 490 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.4.b.a	$152$	$4$	152.b	152.b	$2$	$2$	$2$	$8.968$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots\)
152.4.b.b	$152$	$4$	152.b	152.b	$2$	$56$	$56$	$8.968$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$