Space of modular forms of level 95, weight 5, and Character 95.h

• Label: 95.5.h
• Level: $95$
• Weight: $5$
• Character orbit: 95.h
• Rep. character: $\chi_{95}(69,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $50$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(50\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(95, [\chi])\).

	Total	New	Old
Modular forms	84	84	0
Cusp forms	76	76	0
Eisenstein series	8	8	0

Trace form

\( 76 q - 304 q^{4} + 8 q^{5} + 44 q^{6} - 920 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(95, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.5.h.a	$95$	$5$	95.h	95.h	$6$	$76$	$38$	$9.820$		None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$