Space of modular forms of level 95, weight 4, and Character 95.k

• Label: 95.4.k
• Level: $95$
• Weight: $4$
• Character orbit: 95.k
• Rep. character: $\chi_{95}(6,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.k (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(40\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(95, [\chi])\).

	Total	New	Old
Modular forms	192	120	72
Cusp forms	168	120	48
Eisenstein series	24	0	24

Trace form

120 * q - 6 * q^3 + 18 * q^4 - 78 * q^6 + 144 * q^8 + 90 * q^9 - 90 * q^10 + 432 * q^12 + 300 * q^13 + 24 * q^14 - 486 * q^16 - 180 * q^17 - 648 * q^18 - 672 * q^19 - 468 * q^21 - 384 * q^22 + 24 * q^23 - 432 * q^24 + 636 * q^26 + 1734 * q^27 + 1200 * q^28 + 1200 * q^29 + 120 * q^30 + 60 * q^31 - 420 * q^32 - 1062 * q^33 + 12 * q^34 - 390 * q^35 - 2712 * q^36 + 120 * q^37 - 1278 * q^38 - 1608 * q^39 - 720 * q^40 + 276 * q^41 + 810 * q^42 + 84 * q^43 + 6714 * q^44 + 1050 * q^46 + 2052 * q^47 + 4734 * q^48 - 1800 * q^49 + 300 * q^50 + 930 * q^51 - 5430 * q^52 - 348 * q^53 - 5538 * q^54 + 2880 * q^56 - 4512 * q^57 - 2592 * q^58 - 3786 * q^59 + 1980 * q^60 + 7644 * q^61 - 3696 * q^62 + 4620 * q^63 - 492 * q^64 + 2190 * q^65 - 360 * q^66 - 1230 * q^67 + 3942 * q^68 + 1008 * q^69 - 3240 * q^70 - 4380 * q^71 + 12588 * q^72 - 8004 * q^73 + 1560 * q^74 - 1800 * q^75 - 11124 * q^76 + 2736 * q^77 - 14532 * q^78 - 1632 * q^79 - 2640 * q^80 - 8130 * q^81 - 5838 * q^82 + 1320 * q^83 - 108 * q^84 + 720 * q^85 + 3210 * q^86 - 2436 * q^87 + 7056 * q^88 + 4452 * q^89 + 9750 * q^90 + 11748 * q^91 + 732 * q^92 + 9576 * q^93 + 11088 * q^94 + 14340 * q^96 + 9954 * q^97 + 10308 * q^98 - 744 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(95, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.4.k.a	$95$	$4$	95.k	19.e	$9$	$60$	$10$	$5.605$		None		✓			95.4.k.a	$2$	$0$	\(-9\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
95.4.k.b	$95$	$4$	95.k	19.e	$9$	$60$	$10$	$5.605$		None		✓			95.4.k.b	$2$	$0$	\(9\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{4}^{\mathrm{old}}(95, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(95, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)