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

• Label: 95.2.l
• Level: $95$
• Weight: $2$
• Character orbit: 95.l
• Rep. character: $\chi_{95}(8,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $20$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(20\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	48	48	0
Cusp forms	32	32	0
Eisenstein series	16	16	0

Trace form

32 * q - 6 * q^2 - 6 * q^3 - 4 * q^5 - 8 * q^6 - 12 * q^7 - 6 * q^10 - 8 * q^11 - 6 * q^13 - 24 * q^15 + 12 * q^16 + 6 * q^17 + 16 * q^20 + 12 * q^21 + 6 * q^22 - 14 * q^23 - 8 * q^25 + 32 * q^26 + 28 * q^28 + 28 * q^30 - 36 * q^32 + 26 * q^35 - 64 * q^36 + 50 * q^38 - 72 * q^40 - 48 * q^41 - 42 * q^42 + 4 * q^43 - 16 * q^45 + 24 * q^47 + 48 * q^48 + 60 * q^51 - 18 * q^52 + 12 * q^53 - 4 * q^55 + 48 * q^57 - 68 * q^58 + 114 * q^60 + 36 * q^61 + 4 * q^62 + 30 * q^63 - 100 * q^66 + 18 * q^67 - 108 * q^68 + 18 * q^70 - 12 * q^71 + 132 * q^72 - 30 * q^73 - 76 * q^76 + 20 * q^77 + 84 * q^78 + 42 * q^80 - 12 * q^81 + 32 * q^82 - 4 * q^83 - 54 * q^85 + 72 * q^86 - 100 * q^87 + 72 * q^90 - 84 * q^91 + 4 * q^92 + 24 * q^93 - 34 * q^95 - 48 * q^96 - 72 * q^98

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.l.a	$95$	$2$	95.l	95.l	$12$	$4$	$1$	$0.759$	\(\Q(\zeta_{12})\)	None		✓			95.2.l.a	$4$	$1$	\(-6\)	\(-6\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{2}+\cdots\)
95.2.l.b	$95$	$2$	95.l	95.l	$12$	$4$	$1$	$0.759$	\(\Q(\zeta_{12})\)	None		✓			95.2.l.b	$4$	$0$	\(0\)	\(-6\)	\(2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1-\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{3}+\cdots\)
95.2.l.c	$95$	$2$	95.l	95.l	$12$	$24$	$6$	$0.759$		None		✓	✓		95.2.l.c	$4$	$0$	\(0\)	\(6\)	\(-2\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$