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 - 300 * q^10 - 212 * q^11 + 108 * q^14 + 12 * q^15 - 2068 * q^16 - 184 * q^19 + 108 * q^20 + 1668 * q^21 + 2962 * q^24 - 592 * q^25 - 1348 * q^26 + 1974 * q^29 + 4044 * q^30 - 1614 * q^34 + 3372 * q^35 - 5444 * q^36 - 2188 * q^39 - 1416 * q^40 + 2802 * q^41 + 10554 * q^44 - 7548 * q^45 - 22704 * q^49 + 14988 * q^51 - 5604 * q^54 - 428 * q^55 - 9402 * q^59 + 6318 * q^60 - 13192 * q^61 + 37980 * q^64 - 20910 * q^66 - 19188 * q^70 + 46524 * q^71 + 7904 * q^74 + 38166 * q^76 - 6426 * q^79 + 17104 * q^80 + 9234 * q^81 + 12510 * q^85 - 28068 * q^86 - 9240 * q^89 + 13452 * q^90 + 56016 * q^91 - 12142 * q^95 - 128276 * q^96 + 1922 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.5.h.a	$95$	$5$	95.h	95.h	$6$	$76$	$38$	$9.820$		None		✓	✓	✓	95.5.h.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$