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

• Label: 95.2.b
• Level: $95$
• Weight: $2$
• Character orbit: 95.b
• Rep. character: $\chi_{95}(39,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $20$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	12	8	4
Cusp forms	8	8	0
Eisenstein series	4	0	4

Trace form

8 * q - 6 * q^4 - 3 * q^5 - 8 * q^9 + 8 * q^10 - 6 * q^11 - 12 * q^14 + 10 * q^15 - 6 * q^16 + 4 * q^19 + 8 * q^20 + 20 * q^21 - 8 * q^24 - 3 * q^25 + 12 * q^26 - 24 * q^29 + 24 * q^30 - 8 * q^31 + 16 * q^34 + 5 * q^35 - 26 * q^36 + 8 * q^39 - 4 * q^40 - 8 * q^41 - 28 * q^44 - 21 * q^45 + 4 * q^46 + 10 * q^49 + 4 * q^50 + 4 * q^51 + 16 * q^54 - 25 * q^55 + 52 * q^56 - 20 * q^59 + 20 * q^60 - 10 * q^61 - 2 * q^64 - 12 * q^65 - 48 * q^66 + 24 * q^69 + 16 * q^70 + 60 * q^71 + 20 * q^74 - 34 * q^75 - 10 * q^76 + 16 * q^79 - 30 * q^80 + 56 * q^81 + 24 * q^84 + 29 * q^85 - 20 * q^86 - 20 * q^89 - 40 * q^90 - 32 * q^91 + 36 * q^94 + q^95 - 64 * q^96 + 6 * 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.b.a	$95$	$2$	95.b	5.b	$2$	$2$	$2$	$0.759$	\(\Q(\sqrt{-1}) \)	None		✓			95.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+(2 i-1)q^{5}-2 i q^{7}+\cdots\)
95.2.b.b	$95$	$2$	95.b	5.b	$2$	$6$	$6$	$0.759$	6.0.16516096.1	None		✓	✓		95.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)