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

• Label: 95.5.n
• Level: $95$
• Weight: $5$
• Character orbit: 95.n
• Rep. character: $\chi_{95}(21,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $156$
• Newform subspaces: $1$
• Sturm bound: $50$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.n (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
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	252	156	96
Cusp forms	228	156	72
Eisenstein series	24	0	24

Trace form

156 * q + 24 * q^3 + 42 * q^4 + 42 * q^6 - 504 * q^9 - 150 * q^10 - 1728 * q^12 - 1122 * q^13 + 576 * q^14 + 2058 * q^16 + 1260 * q^17 + 900 * q^19 + 1026 * q^21 - 4608 * q^22 - 1260 * q^23 - 4032 * q^24 + 3672 * q^26 - 2448 * q^27 + 4992 * q^28 + 1494 * q^29 - 4200 * q^30 + 5616 * q^31 + 11700 * q^32 + 2430 * q^33 + 15300 * q^34 + 1800 * q^35 + 13392 * q^36 + 9414 * q^38 - 12504 * q^39 - 2400 * q^40 - 15120 * q^41 - 36834 * q^42 + 5586 * q^43 - 61398 * q^44 - 8910 * q^46 + 3870 * q^47 + 57462 * q^48 - 16014 * q^49 + 25116 * q^51 + 6642 * q^52 + 21312 * q^53 - 14226 * q^54 - 8166 * q^57 - 10752 * q^58 - 16686 * q^59 - 18900 * q^60 - 58092 * q^61 - 6120 * q^62 - 60702 * q^63 + 33132 * q^64 + 16200 * q^65 + 41916 * q^66 + 41406 * q^67 + 9630 * q^68 + 65826 * q^69 + 41400 * q^70 + 28296 * q^71 + 76524 * q^72 + 2790 * q^73 - 32004 * q^74 + 5580 * q^76 - 5508 * q^77 - 22620 * q^78 + 5334 * q^79 - 32400 * q^80 - 55848 * q^81 - 68154 * q^82 - 8280 * q^83 - 84564 * q^84 - 33600 * q^85 + 20178 * q^86 - 28968 * q^87 - 13104 * q^88 - 13212 * q^89 - 28650 * q^90 + 122592 * q^91 + 57708 * q^92 + 93744 * q^93 - 211236 * q^96 + 18966 * q^97 + 13968 * q^98 + 28038 * 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.n.a	$95$	$5$	95.n	19.f	$18$	$156$	$26$	$9.820$		None		✓	✓	✓	95.5.n.a	$2$	$0$	\(0\)	\(24\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{5}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(95, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)