Space of modular forms of level 152, weight 5, and Character 152.k

• Label: 152.5.k
• Level: $152$
• Weight: $5$
• Character orbit: 152.k
• Rep. character: $\chi_{152}(11,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $156$
• Newform subspaces: $2$
• Sturm bound: $100$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	152.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(100\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(152, [\chi])\).

	Total	New	Old
Modular forms	164	164	0
Cusp forms	156	156	0
Eisenstein series	8	8	0

Trace form

\( 156 q - q^{2} - 2 q^{3} - 15 q^{4} + 13 q^{6} - 94 q^{8} - 2000 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(152, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.5.k.a	$152$	$5$	152.k	152.k	$6$	$4$	$2$	$15.712$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(-8\)	\(-14\)	\(0\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{U}(1)[D_{6}]$	\(q+(-4+4\beta _{1})q^{2}+(-7+7\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
152.5.k.b	$152$	$5$	152.k	152.k	$6$	$152$	$76$	$15.712$		None		$4$	$0$	\(7\)	\(12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$