Space of modular forms of level 152, weight 2, and Character 152.o

• Label: 152.2.o
• Level: $152$
• Weight: $2$
• Character orbit: 152.o
• Rep. character: $\chi_{152}(27,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

	Total	New	Old
Modular forms	44	44	0
Cusp forms	36	36	0
Eisenstein series	8	8	0

Trace form

\( 36 q - 3 q^{2} - 6 q^{3} + q^{4} - 7 q^{6} + 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.2.o.a	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.b	$152$	$2$	152.o	152.o	$6$	$4$	$2$	$1.214$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.c	$152$	$2$	152.o	152.o	$6$	$28$	$14$	$1.214$		None		$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$