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

• Label: 95.4.b
• Level: $95$
• Weight: $4$
• Character orbit: 95.b
• Rep. character: $\chi_{95}(39,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $2$
• Sturm bound: $40$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(40\)
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	32	28	4
Cusp forms	28	28	0
Eisenstein series	4	0	4

Trace form

28 * q - 120 * q^4 + 2 * q^5 + 16 * q^6 - 220 * q^9 + 8 * q^10 + 52 * q^11 + 16 * q^14 + 24 * q^15 + 344 * q^16 - 76 * q^19 + 32 * q^20 + 80 * q^21 - 8 * q^24 + 46 * q^25 - 8 * q^26 + 376 * q^29 - 4 * q^30 - 784 * q^31 + 120 * q^34 + 38 * q^35 + 856 * q^36 - 840 * q^39 - 660 * q^40 + 40 * q^41 - 184 * q^44 + 298 * q^45 - 408 * q^46 - 128 * q^49 + 1364 * q^50 - 832 * q^51 - 1776 * q^54 + 1462 * q^55 + 760 * q^56 + 1336 * q^59 + 156 * q^60 - 204 * q^61 - 1496 * q^64 + 2564 * q^65 + 1944 * q^66 - 1000 * q^69 + 544 * q^70 + 120 * q^71 - 5712 * q^74 + 2116 * q^75 + 760 * q^76 - 536 * q^79 + 3700 * q^80 - 236 * q^81 - 2960 * q^84 - 2386 * q^85 - 1984 * q^86 + 3480 * q^89 - 796 * q^90 + 656 * q^91 - 6472 * q^94 + 266 * q^95 + 4144 * q^96 - 3532 * 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.b.a	$95$	$4$	95.b	5.b	$2$	$12$	$12$	$5.605$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			95.4.b.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6})q^{3}+(-3+\beta _{2}+\cdots)q^{4}+\cdots\)
95.4.b.b	$95$	$4$	95.b	5.b	$2$	$16$	$16$	$5.605$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		95.4.b.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{2}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-5+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)