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

• Label: 152.4.o
• Level: $152$
• Weight: $4$
• Character orbit: 152.o
• Rep. character: $\chi_{152}(27,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $116$
• 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.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
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	124	124	0
Cusp forms	116	116	0
Eisenstein series	8	8	0

Trace form

\( 116 q - 3 q^{2} - 6 q^{3} - 7 q^{4} - 23 q^{6} + 484 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.4.o.a	$152$	$4$	152.o	152.o	$6$	$4$	$2$	$8.968$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		✓			152.4.o.a	$4$	$0$	\(0\)	\(-30\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b	$152$	$4$	152.o	152.o	$6$	$112$	$56$	$8.968$		None		✓	✓		152.4.o.b	$4$	$0$	\(-3\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$