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

• Label: 95.4.e
• Level: $95$
• Weight: $4$
• Character orbit: 95.e
• Rep. character: $\chi_{95}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $40$
• Newform subspaces: $3$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(40\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	64	40	24
Cusp forms	56	40	16
Eisenstein series	8	0	8

Trace form

40 * q + 4 * q^2 + 2 * q^3 - 86 * q^4 + 26 * q^6 - 40 * q^7 - 96 * q^8 - 210 * q^9 + 50 * q^10 - 72 * q^11 + 48 * q^12 + 48 * q^13 + 84 * q^14 + 60 * q^15 - 302 * q^16 - 264 * q^17 - 400 * q^18 + 464 * q^19 + 132 * q^21 + 108 * q^22 + 156 * q^23 + 244 * q^24 - 500 * q^25 + 612 * q^26 + 788 * q^27 + 556 * q^28 - 60 * q^29 - 80 * q^30 - 8 * q^31 + 998 * q^32 + 1430 * q^33 - 1462 * q^34 + 130 * q^35 - 2020 * q^36 - 2096 * q^37 + 1450 * q^38 - 1904 * q^39 + 720 * q^40 - 136 * q^41 - 978 * q^42 - 460 * q^43 - 584 * q^44 + 160 * q^45 + 1988 * q^46 + 696 * q^47 - 1522 * q^48 + 3980 * q^49 - 200 * q^50 + 1360 * q^51 + 850 * q^52 - 392 * q^53 - 458 * q^54 - 2776 * q^56 - 956 * q^57 - 564 * q^58 - 786 * q^59 + 810 * q^60 + 1424 * q^61 - 112 * q^62 + 1032 * q^63 + 4288 * q^64 - 200 * q^65 + 864 * q^66 + 1702 * q^67 + 1260 * q^68 + 1096 * q^69 - 260 * q^70 + 676 * q^71 - 1744 * q^72 - 1162 * q^73 - 4104 * q^74 - 100 * q^75 - 3176 * q^76 - 3888 * q^77 + 4296 * q^78 - 536 * q^79 - 1600 * q^80 + 356 * q^81 + 2270 * q^82 - 3764 * q^83 - 1720 * q^84 + 120 * q^85 + 496 * q^86 + 1760 * q^87 + 1412 * q^88 - 1674 * q^89 + 890 * q^90 - 356 * q^91 - 4088 * q^92 + 156 * q^93 - 2412 * q^94 - 260 * q^95 - 11736 * q^96 - 1790 * q^97 + 12762 * q^98 + 3298 * 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.e.a	$95$	$4$	95.e	19.c	$3$	$2$	$1$	$5.605$	\(\Q(\sqrt{-3}) \)	None		✓			95.4.e.a	$2$	$0$	\(1\)	\(5\)	\(-5\)	\(44\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots\)
95.4.e.b	$95$	$4$	95.e	19.c	$3$	$18$	$9$	$5.605$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None		✓			95.4.e.b	$2$	$0$	\(6\)	\(2\)	\(-45\)	\(-90\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
95.4.e.c	$95$	$4$	95.e	19.c	$3$	$20$	$10$	$5.605$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓		95.4.e.c	$2$	$0$	\(-3\)	\(-5\)	\(50\)	\(6\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(4\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

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

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