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

• Label: 95.5.f
• Level: $95$
• Weight: $5$
• Character orbit: 95.f
• Rep. character: $\chi_{95}(58,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $50$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	95.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
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	72	12
Cusp forms	76	72	4
Eisenstein series	8	0	8

Trace form

72 * q + 20 * q^3 - 66 * q^5 - 128 * q^6 + 130 * q^7 + 16 * q^10 + 312 * q^11 - 80 * q^12 - 760 * q^13 + 1184 * q^15 - 3504 * q^16 + 1110 * q^17 + 960 * q^20 - 2840 * q^21 + 720 * q^22 + 300 * q^23 - 2322 * q^25 - 192 * q^26 + 2060 * q^27 - 1120 * q^28 - 1160 * q^30 - 584 * q^31 - 6600 * q^32 + 3200 * q^33 - 4602 * q^35 + 10160 * q^36 + 2280 * q^37 + 11736 * q^40 + 6984 * q^41 - 8800 * q^42 - 8110 * q^43 - 8748 * q^45 + 11312 * q^46 - 3870 * q^47 - 660 * q^48 + 588 * q^50 + 7224 * q^51 + 2340 * q^52 + 13380 * q^53 - 5048 * q^55 - 13416 * q^56 + 5280 * q^58 - 9684 * q^60 + 10952 * q^61 - 1800 * q^62 + 17830 * q^63 + 852 * q^65 - 37928 * q^66 + 13780 * q^67 - 39000 * q^68 + 26500 * q^70 + 28680 * q^71 + 52900 * q^72 + 24070 * q^73 - 10208 * q^75 - 13530 * q^77 + 9400 * q^78 + 60240 * q^80 - 78720 * q^81 - 40360 * q^82 - 1740 * q^83 - 10112 * q^85 + 6432 * q^86 + 9720 * q^87 - 48180 * q^88 - 52736 * q^90 - 34232 * q^91 - 25800 * q^92 + 23800 * q^93 - 6498 * q^95 + 88440 * q^96 + 38060 * q^97 - 31440 * q^98

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.f.a	$95$	$5$	95.f	5.c	$4$	$72$	$36$	$9.820$		None		✓	✓	✓	95.5.f.a	$2$	$0$	\(0\)	\(20\)	\(-66\)	\(130\)		$\mathrm{SU}(2)[C_{4}]$

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

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