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

• Label: 95.2.g
• Level: $95$
• Weight: $2$
• Character orbit: 95.g
• Rep. character: $\chi_{95}(18,\cdot)$
• Character field: $\Q(\zeta_{4})$
• 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.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(i)\)
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 - 2 * q^5 - 16 * q^6 - 6 * q^7 - 16 * q^11 + 12 * q^16 + 6 * q^17 + 32 * q^20 - 4 * q^23 - 22 * q^25 + 16 * q^26 + 8 * q^28 - 40 * q^30 - 14 * q^35 + 4 * q^36 + 4 * q^38 + 2 * q^43 + 40 * q^45 - 18 * q^47 + 40 * q^55 - 88 * q^58 - 24 * q^61 + 8 * q^62 + 78 * q^63 - 8 * q^66 + 72 * q^68 + 6 * q^73 - 20 * q^76 - 62 * q^77 - 36 * q^80 + 24 * q^81 + 88 * q^82 - 68 * q^83 + 88 * q^87 - 4 * q^92 - 96 * q^93 - 14 * q^95 + 24 * q^96

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.g.a	$95$	$2$	95.g	95.g	$4$	$4$	$2$	$0.759$	\(\Q(i, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)		✓			95.2.g.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q-2\beta _{2}q^{4}-\beta _{3}q^{5}+(2-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
95.2.g.b	$95$	$2$	95.g	95.g	$4$	$12$	$6$	$0.759$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		95.2.g.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(-12\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-\beta _{6}-\beta _{8})q^{4}+\cdots\)