Space of modular forms of level 95, weight 2, and Character 95.e

• Label: 95.2.e
• Level: $95$
• Weight: $2$
• Character orbit: 95.e
• Rep. character: $\chi_{95}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(20\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(95, [\chi])\).

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

Trace form

16 * q - 2 * q^2 - 2 * q^3 - 10 * q^4 + 4 * q^6 - 12 * q^7 + 12 * q^8 - 6 * q^9 - 8 * q^11 + 12 * q^12 + 6 * q^13 - 6 * q^14 - 4 * q^15 - 14 * q^16 - 6 * q^17 + 8 * q^18 - 2 * q^19 + 8 * q^21 + 6 * q^22 - 6 * q^23 - 2 * q^24 - 8 * q^25 - 4 * q^26 + 16 * q^27 + 6 * q^29 + 16 * q^30 - 16 * q^31 - 24 * q^32 - 24 * q^33 + 10 * q^34 + 2 * q^35 + 6 * q^36 + 8 * q^37 - 6 * q^38 + 12 * q^39 - 18 * q^40 + 16 * q^41 + 38 * q^42 + 4 * q^43 + 36 * q^44 - 8 * q^45 - 24 * q^46 - 16 * q^48 - 16 * q^49 + 4 * q^50 - 4 * q^51 + 42 * q^52 + 24 * q^54 - 52 * q^56 - 28 * q^57 - 68 * q^58 + 14 * q^59 - 6 * q^60 + 4 * q^61 - 24 * q^62 - 2 * q^63 + 80 * q^64 + 40 * q^65 + 2 * q^66 + 14 * q^67 + 76 * q^68 - 28 * q^69 + 8 * q^70 + 12 * q^71 - 28 * q^72 + 34 * q^73 - 18 * q^74 + 4 * q^75 + 46 * q^76 - 28 * q^77 - 12 * q^78 + 2 * q^79 + 20 * q^81 - 52 * q^82 + 20 * q^83 - 128 * q^84 + 8 * q^85 + 24 * q^86 + 4 * q^87 - 32 * q^88 + 18 * q^89 + 24 * q^90 + 12 * q^91 - 40 * q^92 - 12 * q^93 - 20 * q^94 - 12 * q^95 + 76 * q^96 - 16 * q^97 - 32 * q^98 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(95, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
95.2.e.a	$95$	$2$	95.e	19.c	$3$	$2$	$1$	$0.759$	\(\Q(\sqrt{-3}) \)	None		✓			95.2.e.a	$2$	$0$	\(0\)	\(2\)	\(1\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
95.2.e.b	$95$	$2$	95.e	19.c	$3$	$6$	$3$	$0.759$	6.0.3518667.1	None		✓			95.2.e.b	$2$	$0$	\(-1\)	\(-1\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3}-\beta _{5})q^{3}+(-3+\cdots)q^{4}+\cdots\)
95.2.e.c	$95$	$2$	95.e	19.c	$3$	$8$	$4$	$0.759$	8.0.4601315889.1	None		✓	✓		95.2.e.c	$2$	$0$	\(-1\)	\(-3\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{7}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)