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

• Label: 95.2.i
• Level: $95$
• Weight: $2$
• Character orbit: 95.i
• Rep. character: $\chi_{95}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
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	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

16 * q + 6 * q^4 - 12 * q^6 + 2 * q^9 - 2 * q^10 + 6 * q^14 - 4 * q^15 - 6 * q^16 + 2 * q^19 - 32 * q^20 - 20 * q^21 + 2 * q^24 - 60 * q^26 + 6 * q^29 + 12 * q^30 + 32 * q^31 + 2 * q^34 + 16 * q^35 + 26 * q^36 + 4 * q^39 + 10 * q^40 - 16 * q^41 + 16 * q^44 + 48 * q^45 + 56 * q^46 - 40 * q^49 - 40 * q^50 - 40 * q^51 - 4 * q^54 - 20 * q^55 + 92 * q^56 + 38 * q^59 + 4 * q^60 + 16 * q^61 + 56 * q^64 - 24 * q^65 - 6 * q^66 - 36 * q^69 + 62 * q^70 - 14 * q^74 - 56 * q^75 - 74 * q^76 + 26 * q^79 - 30 * q^80 - 32 * q^81 - 96 * q^84 + 10 * q^85 + 8 * q^86 + 14 * q^89 - 32 * q^90 + 8 * q^91 - 108 * q^94 + 62 * q^95 + 52 * q^96 - 24 * 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.i.a	$95$	$2$	95.i	95.i	$6$	$4$	$2$	$0.759$	\(\Q(\zeta_{12})\)	None		✓			95.2.i.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta_1 q^{2}+2\beta_{2} q^{4}+(-\beta_{2}-\beta_1+1)q^{5}+\cdots\)
95.2.i.b	$95$	$2$	95.i	95.i	$6$	$12$	$6$	$0.759$	12.0.\(\cdots\).2	None		✓	✓		95.2.i.b	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{2}+(\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)